Villa have won just twice in 12 league games since Lambert replaced Alex McLeish in the summer, and they go into Saturday's home game with Arsenal in a relegation place.
But the Villa Park crowd has so far gone easier on the Scot than on his predecessor, and Lambert said: "The fans have been brilliant with me.
"I understand it's not where you want to be and the fans have every right to voice their opinion. But they have been brilliant with me and all I can ask for is to stick with us.
"The bottom three is not where I want to be, that's for sure. Myself, the club or the fans don't want to be there or near that. But I also know the bigger picture and it's not just a quick fix.
"Some of the performances have been very good. We've just not had that break, that little bit of luck to go your way. There have not been too many times when I've walked away and been disappointed with the way we've played."