Not this time. Although they could have done, they really could.
Two years on from their amazing march to the knockout stages of the European Championship, and historic humiliation of England, Iceland failed to repeat the feat at the World Cup last night.
But there was no shame in falling short for the tournament’s smallest ever nation after what was a thrilling, see-saw climax to Group D that saw them thunderclapped from the field by their army of supporters.
An evening which began with them needing to score at least two goals, became one in which they needed one, then two, then three, then two and then one, while throwing everything they had at Croatia to get a result that might even have ended the international career of Lionel Messi and set up a revenge mission against Euro 2016 conquerors France.
They eventually succumbed to opponents who got away with resting nine players but who surely have a chance of emulating the history-making feats of their own most celebrated team, which finished third at the 1998 World Cup.
Iceland had almost no margin for error if they were to escape from a group in which the possible permutations would tax even the finest of mathematical minds.
For, not only did they need to win and for Nigeria not to in the other Group D finale against Argentina, but they also needed the Africans not to lose by a bigger margin than they themselves beat Croatia.
A draw in St Petersburg and Iceland would have had to win by at least two goals; neither was it completely impossible for them to finish dead level with Messi and co and lots to be drawn.
Having all but won the group before last night’s game, Croatia made nine changes, with only captain Luka Modric and Ivan Perisic starting from the side already into the last 16.
Iceland manager Heimir Hallgrímsson argued before the game that playing hungry understudies would make his side’s task harder but the opposite was surely true for a team that had beaten their opponents en route to topping their qualifying group.
They also had the support of the crowd at a venue where three of their squad play their club football, highlighted by an early stadium-wide thunderclap.
That came during a break in play when Birkir Bjarnason took an elbow to the nose from Marko Pjaca and was forced was forced to leave the field for several minutes, during which time word spread Messi had scored for Argentina.
Croatia were playing risk-free football - even against 10 men - content to starve their opponents of the ball in a ploy that worked up to a point.
That was until, like England two years ago, they were rattled by the first long throw from Aron Gunnarson, which Hordor Magnusson flicked across goal.
Buoyed, Iceland began to get in their opponents’ faces, cultimating in a hat-trick of chances moments before half-time.
Alfred Finnbogason fired narrowly wide after robbing Milan Badelj and playing a one-two with Gylfi Sigurdsson, and Lovre Kalinic blocked Bjarnason’s shot after spilling a corner before spectacularly repelling Gunnarsson’s curling exocet.
But the one goal they needed to qualify became three within minutes of the restart when Nigeria equalised against Argentina and they themselves fell behind.
Badelj had just struck the crossbar from 20 yards when Josip Pivaric burst into the box before cutting back a deflected cross his team-mate struck first time in the ground and past Hannes Halldorsson.
A Herculean task was almost immediately made easier when another long throw caused chaos in the Croatia box, with Sverrir Ingason’s header tipped over by Kalinic.
Ingason went even closer from the resulting Sigurdsson corner, jumping highest and hitting the crossbar.
Bjarnason fluffed another great chance from Finnbogason’s cross before the lifeline arrived, Croatia substitute Dejan Lovren handling Sigurdsson’s cross in the box.
Having missed from the spot against Nigeria, the Everton midfielder rammed his penalty straight down the middle.
The thunderclaps were coming thick and fast, and when Argentina scored again, suddenly Iceland were back to needing just one goal to qualify.
But as they desperately threw men on to find a winner, they left too much space at the back and Perisic wandered into it before rifling home left footed.
Half time: Iceland 0 Croatia 0
Croatia, who are the classier outfit, started the better, Iceland were a little too respectful. But once they settled, they looked more dangerous, and they created better chances. Croatia, who made 9 changes for this match, are only sporadically engaged. Iceland want it bad.
Kickoff!
Let's play.
Iceland: Halldorsson, Saevarsson, Ingason, Ragnar Sigurdsson, Magnusson, Gunnarsson, Hallfredsson, Johann Berg Gudmundsson, Gylfi Sigurdsson, Bjarnason, Finnbogason. Subs: Schram, Fridjonsson, Albert Gudmundsson, Sigurdarson, Arnason, Eyjolfsson, Olafur Ingi Skulason, Gislason, Traustason, Bodvarsson, Ari Freyr Skulason, Runarsson.
Croatia: Lovre Kalinic, Jedvaj, Corluka, Caleta-Car, Pivaric, Modric, Badelj, Pjaca, Kovacic, Perisic, Kramaric. Subs: Livakovic, Vrsaljko, Strinic, Lovren, Rakitic, Brozovic, Bradaric, Mandzukic, Rebic, Vida, Subasic.
Referee: Antonio Miguel Mateu Lahoz (Spain)
It's all a bit complex in terms of who needs what
So this handy guide might be a handy guide.
Croatia have already qualified and would need a remarkable collapse to finish anywhere but top. The race for second is complicated. Nigeria will definitely qualify if they beat Argentina; if they draw, they will still go through provided Iceland do not beat Croatia, or win by more than a two-goal margin. If Iceland and Argentina both win, it would come down to goal difference, with Argentina needing to win by at least one more goal than Iceland to overhaul them. A draw is no good to either of them.
Iceland vs Croatia teams
Iceland: Halldorsson, Saevarsson, Ingason, Ragnar Sigurdsson, Magnusson, Gunnarsson, Hallfredsson, Johann Berg Gudmundsson, Gylfi Sigurdsson, Bjarnason, Finnbogason. Subs: Schram, Fridjonsson, Albert Gudmundsson, Sigurdarson, Arnason, Eyjolfsson, Olafur Ingi Skulason, Gislason, Traustason, Bodvarsson, Ari Freyr Skulason, Runarsson.
Croatia: Lovre Kalinic, Jedvaj, Corluka, Caleta-Car, Pivaric, Modric, Badelj, Pjaca, Kovacic, Perisic, Kramaric. Subs: Livakovic, Vrsaljko, Strinic, Lovren, Rakitic, Brozovic, Bradaric, Mandzukic, Rebic, Vida, Subasic.
Referee: Antonio Miguel Mateu Lahoz (Spain)
Who to support, then?
Croatia, got some lovely players, seem like a decent group. Fans, however, have shown tendency to be a bit awful. Are already qualified, and (barring something bizarre) are going to go through top. See permutations here.
Iceland: been there on holiday and it was great. Beat England, which was HILARIOUS. Would be quite funny to see Argentina out. Nigeria were so pathetic in their opening game that they are dead to me. All in all, I'd love Iceland to go through.
Verdict: come on Iceland.
Iceland scouting report!
Who are we keeping our eye upon then?
Alfred Finnbogason is the danger man up front. Aron Gunnarsson, the midfield general actually looks like a Viking, puts it about a bit in midfield and can launch a dangerous long throw. Johann Berg Gudmundsson, a talented right-sider who missed the last match, has shown us at Burnley that he is an exciting player with a bit of quality. Ragnar Sigurdsson, the centre half, is hewn from volcanic rock and is looking to put getting booted in the head in the last match behind him.
I fancied Croatia
as an outside bet for the tournament but instead went for Portugal at 25/1 each way. The VAR nonsense last night, which meant that Portugal are in the much harder side of the draw, was a pain.
Like Portugal, Croatia have plenty of experience. Croatia also have quality, grown-up players all over the park. They have Modric, whom I have hardly ever seen have a bad game. Alongside Ivan Rakitic, that is a central midfield pair the equal of anything in the tournament, bar (arguably) Spain and Germany.
They normally play a 4-2-3-1 and I think Iceland have really got their work cut out. If Mario Mandzukic was a bit less of a plank up front, I'd say Croatia are as good as anyone on their day.
HOOO! HOOO!
Iceland: what a country, what a people, what an expensive but amazing place to go on holiday. The land of ice deserts, hot springs, and spurting geysers has a population, as we all know by now, of just 14 people, and each and everyone of them is looking forward to giving Luka Modric and Croatia a tough, tough match. The smallest nation ever to reach the Finals, 335,000 people are absolutely bang up for this one.
Iceland have passion, teamwork, and excellent support. And they also have plenty of experience of facing this highly talented Croatia side. Iceland's head coach Heimir Hallgrimsson: "We've played Croatia four times in four years, we've often said we're like a married couple - we're trying to get divorced, but we always meet up again."
They had the better of Croatia 1-0 in Reykjavik 12 months ago. But iceland need results to go their way this time. The permutations in Group D are as follows.
If Nigeria win, Iceland are out. If Nigeria score, Iceland need to score at least twice. I suspect we might be hearing the odd HOOO for Argentina as well tonight. The other match, kicking off also at 7pm on the BBC, is Argentina and Nigeria. Surely Argentina and Lionel Messi have to pull their finger out?
The action will take place in the Rostov Arena.
How do you think it will go?