Lambert said: "It was an excellent performance and I don't think there was any doubt we deserved to win the game.
"Bristol City are a good side and made it tough for us but I thought we were terrific right from the very first minute and continued where we left off at Leicester last week.
"I've got good players who want to win games and if we keep the stadium rocking then we'll have a chance. Everyone's got a roll to play, the fans, the players, everybody.
"It's a tremendous result for us and the lads have been terrific again. But it's nothing I haven't seen before.
"They always keep going right to the very end. They are a group that will always go to the final bell for you and that's a great thing to have.
"They have got a great hunger and a great drive to win games. Everyone was excellent. I couldn't single anyone out.
"Don't say we're in the driving seat though. We are only three points clear (of the third place side) and there's miles to go yet. Absolute miles."
Bristol City counterpart Keith Millen blamed a poor start to the game for their loss.
Millen said: "All your plans go out of the window when you make a start like that. It put us on the back foot, allowed Norwich to settle, and to be honest we found it hard and had to defend for our lives.
"The ball just kept coming back at us. We changed it a bit in the second half, started to press the ball higher up the pitch and began to cause them problems.
"We got our goal and at one all I thought it could have gone either way. We had our chances but we were often wasteful in good positions.
"But it's only fair to say that Norwich had a lot of opportunities too. To be honest they looked dangerous the whole night and you have got to give them a lot of credit for the way they played.
"They are a good side who have really got a lot of self belief. The annoying thing from our point of view is that we conceded three soft goals.
"We got done by two long balls and then were punished right at the end for not clearing our lines.
"Now it's a case of putting this behind us and trying to go on another good run. That's what good sides do."