The Blues put in one of their best performances of the season away at Villa Park to qualify for the fifth round of the FA Cup.
Conor Gallagher and Nicolas Jackson both found the net before Enzo Fernandez capped off the win with a stunning free-kick.
The victory comes off the back of two dire displays in the Premier League, conceding four against Liverpool and Wolves.
Chelsea have turned corners before this season before taking bigger steps back, but away at Villa Park where the home team have been near-perfect this season, there was reason for Pochettino to smile.
Asked if it was their best display of the season, he said: "I think so, we were talking in the dressing room, and I think it was one of the best or maybe the best this season.
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"We're so happy, they played football with joy and that's what pleased us the most.
"The team was all together, ready to compete, ready to fight and you know always it's about energy and attitude and today that was there. I was saying, 'I really believe but you need to believe' and that is about the attitude and fight, and then the talent appeared.
"Today I was more relaxed than ever, because I knew the team was going to perform. I could feel it after Wolves. You really know when the players are with you and the players care for you and want to play for you and this group sometimes they need these types of things to realise it's possible to push yourself and play better."
The Argentine was keen to stress the challenges of coaching such a young team, and used Manchester United legend Keane as an example.
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He explained: "We are a young team and Roy, you know very well that it's about being solid and consistent and that's the most difficult thing in a young team.
"We need a bigger mentality, sometimes the mentality of this guy [points at Keane], but it's about finding a balance.
"For me I am so optimistic, I know at a club like Chelsea people aren't patient and they don't want to know about the circumstances but the reality is another thing, we're not the Chelsea that was competing in a different time."
Pochettino was also asked if he has the hardest job in football, and he didn't disagree.
"You are telling me, but of course it's the most difficult thing," he said. "We're talking about maybe the youngest team in the Premier League and the expectations are so high, so it's normal to sometimes feel pressure.
"It's not easy to manage all of these things. There are too many things that as a coaching staff we are dealing with, and it's difficult to explain to people, but with this type of performance we're really pleased."