The Premier League outfit defeated League One Rotherham United 3-0 in the second round at Villa Park with Andi Weimann, Christian Benteke and Fabian Delph all on target and Lambert was genuinely pleased with the performance.
"You have got to earn the right to win the football match but I thought we would with the team we put out," Lambert said. "Some of the football was excellent. The third goal - the one-touch football was brilliant.
"The squad is really together and strong and we trusted them to go out there and perform and they have been excellent.
"Cup football is a difficult thing because you can play against a small team and they are a totally different animal to what you are used to playing in the league. But we handled it well."
Villa will next meet Premier League rivals Tottenham at Villa Park in the third round.