Lowly Villa crashed to a 2-0 defeat at fellow Premier League strugglers Hull City on Tuesday.
A fifth consecutive league loss saw Villa drop into the bottom three on goal difference, a point adrift of Hull in 15th place.
They went into the match without a win in nine league games and the away fans let their feelings known at the KC Stadium as that became 10, displaying banners calling for the removal of Lambert.
However, the Scot - who said he was understanding of the situation - was sticking to his guns post-match when asked about discontent in the stands.
"I was aware of it months ago. I try to do my best," Lambert told the BBC.
"It's a great football club with a massive fan base and they want to see their team doing well.
"We've got to keep battling away and keep our heads up. We're certainly in a fight. You have to keep going and keep being positive.
"There's a fight, the lads know it. There's a lot of football to be played.
"I am in no doubt we will turn it around. No doubt. As I have said to the players - we have 13 cup finals to get through."
