Villa found themselves outplayed for long periods of the game, but showed great resilience to somehow earn all three points after twice coming from behind to stun City.
Lambert felt the result was all the more impressive considering the players unavailable for him, with the likes of Christian Benteke, Gabriel Agbonlahor, Ashley Westwood and Jores Okore all sidelined for the home side.
"I thought we were oustanding," beamed Lambert.
"The injury list has been pretty horrendous, we've lost two lads [Benteke & Agbonlahor] who have scored a lot of goals for us, we have lost [Ashley] Westwood who has been fantastic for me and [Jores] Okore was starting to find his feet.
"There was a lot going on in the game and we are up against one of the best teams in the country, so that's the magnitude of the result.
"I thought they would change it a bit with the game in midweek against Bayern Munich but it just shows how strong they are. I thought we were outstanding."
Lambert also praised Leandro Bacuna after he played a key role in Villa's success, creating the first goal and then scoring the second with a superb free-kick
"It was brilliant [the free-kick]," added Lambert. "I've seen him do it in training and I thought he did brilliant for the first goal and the second goal was absolute world-class against a top, top goalkeeper."