The fierce rivals played out to a 1-1 draw on Sunday, with a Mohamed Salah wonder-strike ruled out by a Wayne Rooney penalty.
But – despite the final result – the hosts were dominant throughout, registering 23 shots to Everton’s three while holding 79% possession.
Barnes and Gray were commentating on the match for BeinSPORTS, but were quick to descend into an argument on the performances of both teams following the final whistle.
The Reds legend kicked things off, saying: “Everton created absolutely nothing and got a point so they are good.
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“But let’s not get carried away by thinking it was a good performance from Everton.”
Gray – who made 49 appearances for the Toffees between 1983-1985 – fired back with his own jibe: “They are at different parts of the spectrum. Your team should be pretty much nearly the finished article with your coach. This Everton team is in its infancy.”
Barnes continued to slam his rival’s performance, saying: “You still have players who can create chances and should be able to get the ball to create them.”
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But it seemed like his 62-year-old counterpart won the argument by asking: “Who feels better today?”
“Of course, Sam [Allardyce] feels better,” Barnes reluctantly answered.
The result at the weekend leaves Liverpool 16 points behind leaders Manchester City, but they will hope to lessen the gap when they host West Brom tomorrow evening.