"Tough place to come. We played really good. At the end they had one or two chances but we played a fantastic game. A good step for us in this tournament," said Guardiola.
"It's good that not just Erling [Haaland] scored and we had more chances for others. Impact from Rayan Cherki and Tijjani Reijnders good too. Little disappointed with result in Monaco, we created chances and didn't win and played the same as today but today got the goals. Teams in La Liga are really tough and a top-class manager.
“Spanish people know it, maybe English people don’t know it, Villarreal is a top, top team. So I know how difficult it is to come here. Indeed, in the way we played, I have the feeling that, in many ways, we are coming back to what we were in the past.
"Our numbers in the Champions League in the last year are not bad. Personally my numbers are not bad. But last season was tough for us, the vibe and how the team are playing now make me feel fine."
City’s Rico Lewis, who assisted the game’s opening goal for Haaland, told TNT Sports: "We felt in control for most of the game. There's always better things we can do and there were a few spells they had that we could've prevented but we have to be harsh on ourselves if we want to win the competition.
"We've got some confidence back. When you're playing with confidence there's nothing to stop you but yourself. Everyone trusts each other as well and there's nothing better than us having each other's backs."
Speaking about Haaland, he added: "Impossible, amazing. To play with him in the team, he helps us more than people realise. He draws defenders to free other people and then that frees him up to score. He's impossible to defend. He's such a hard worker and never stops wanting to score."