City dominated the first half and deservedly led through Yaya Toure's sixth goal of the season just before the interval.
Lambert said: "I know they had a lot of possession but [Brad] Guzan didn't really have a save, as such.
"They are one of the favourites to win the Premier League, and one of the teams that could win the Champions League.
"That shows the magnitude of this result. They might have rested a few for the Bayern [Munich] game but, if you look at the side, they were a lot of top players.
"It is a big win, three points for us. I am delighted to win."
Lambert, whose side survived a relegation scare last season, was unwilling to say whether it was his best result since taking charge at Villa last year.
He said: "There have been (other) big games and big results, big moments at certain times.
"But this is a fabulous achievement because of the magnitude of their club and the players they have got.
"Where I will say it was very pleasing is that we had to come back twice.
"We have made a really good start in the league.
"We have played Arsenal, Chelsea, Liverpool, then Tottenham in the cup, and then Manchester City.
"It has been one hell of a start but we have come through it and are playing with a lot of confidence."