With fan discontent swirling around Stamford Bridge and the Emirates in recent weeks, the Villa manager is grateful that the Holte End is still behind him and the team.
Lambert said: "The Villa fans have been brilliant to me and they've been like that all season long.
"They could have turned pretty quickly with the results - but they have been excellent.
"They've come in their thousands to watch us home and away. I can't ask any more from the fans, that's for sure.
"You can't keep everybody happy all the time, I understand that, and fans naturally get upset with results.
"But in general terms, the crowd at Aston Villa have been brilliant to me. They pay a lot of money to follow the team and will drive us on as always against Manchester City on Monday.
"It's a great honour to be the manager of the club. It's a massive club with a great history. I've never been one to shy away from things.
"You either roll over and die or meet things head on and I'm not going to roll over."
Lambert insists Villa will not be intimidated ahead of the Sky Live clash despite a 5-0 defeat at the Etihad Stadium earlier this season.
"I don't think we go into any game frightened of anyone," he added. "We have to take the challenge on. We know how good a side they are.
"We have to go into it as if we can win it. There's no point in playing otherwise. We're certainly playing well enough to cause them trouble."