"Our team is very hungry and humble," Man-of-the-Match Giovani Lo Celso told Movistar Plus. "But we faced one of the best teams in the world and we go out with the sensation that we should have scored several more goals.
"We knew that we needed to shorten the field for them - they are a team that can't have spaces to work the ball. We played our game, we are a team that always try to be the protagonist and we had a lot of opportunities to win by a bigger margin."
Villarreal coach Unai Emery has won a record four Europa League titles - three with Sevilla - and his current side looks to have inherited his DNA and adapted it to the Champions League in their efforts to compete toe-to-toe with the leading clubs.
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They eliminated Juventus in the last 16 and have now shocked Bayern, who were unbeaten in this year's competition and tasted their first Champions League defeat away from home since 2017.
The build-up to Villarreal's winner started with Moreno, who is the heart and soul of the Yellow Submarine.
He received the ball close to the right touchline and played it through to Lo Celso whose low cross was struck the first time by Dani Parejo. Neuer looked to have it covered but Danjuma got there first and stroked the ball home from close range.
"We know that it will be a completely different game in Germany," captain Parejo told reporters.
"We had at least five opportunities to score, they didn't create a single one. That says a lot about what we are capable of. So we will go there and compete with the same passion."