Lambert's side head into Saturday's clash with Swansea looking to halt a run of four successive defeats that has seen them slide to within three points of the Barclays Premier League relegation zone.
Home form has been the biggest problem, with Villa picking up only seven points and scoring just six goals, the worst record in the top four divisions.
They have found the net in only one of their last six home matches and the fans made their feelings clear as Villa slumped to a 1-0 defeat by Crystal Palace on Boxing Day.
Lambert conceded expectations are not making life easier, saying: "The lads are edgy on certain things but we have to work on that.
"You can't turn round and be critical of the crowd, that's for sure. It's too big a club.
"It's probably not helping in terms of us trying to play our game at certain times but they pay their money and they're entitled to voice their opinion.
"Football is about giving people something to cheer. We're doing everything we can to keep building what we want to try and do. I'm a million miles short of what I want to do with the club.
"Personally I know what it's like because I've played with big clubs as a footballer. I was never exempt from criticism.
"I remember my first few games at Celtic, I lost them. People were saying go back to Dortmund, 60,000 or whatever it was. Until I bedded myself in and got a grip of it, then it went reasonably okay.
"I know criticism. For the team, when they're young, they need that support through thick and thin.
"Some people talk about bravery of going in for a tackle that's 10 feet high and blood, guts and thunder. Bravery's taking the ball in front of 40,000 or 50,000 in an area where people will just shy away from it.
"As long as they never do that - that's the one thing I can't accept, trying to hide. As long as they keep trying to do the right things, then I'll never criticise them.
"I don't want to be sitting like this every time. It's a challenge I'm not going to wilt under. I've never wilted. You fight it, you don't run away from it."
Michael Laudrup's Swansea sit a point above Villa and are also not in good form having gone five matches without a victory.
"Even if you don't win in one, there's pressure," said Lambert. "Football now, you get one or two games. If you've not won two games, there's a crisis, it's getting shorter and shorter.
"Swansea are on that same kind of run, I'm pretty sure if you asked Michael he'd say the exact same thing. It's a big game for both teams."
Midfielder Ashley Westwood returns from suspension but Lambert is limited in his options, with top scorer Christian Benteke and defender Ron Vlaar still injured.
Goalkeeper Brad Guzan was one of the few players to emerge from the Palace game with credit, and he promised Villa fans the team will give everything to try to stop the rot on Saturday.
The American said: "We understand that the supporters are frustrated, we're frustrated.
"We know that we're going through a bit of a rough patch. There are teams all up and down the country that will, if they haven't already, go through a rough patch and that's what makes the Premier League the Premier League.
"We beat Manchester City here, we beat Arsenal at the Emirates, so we've picked up some positive results and that's what we're going to lean on.
"We have to stay confident, we're together, we're in this with the supporters as well. We need to make this right.
"Four games doesn't make you a bad team. We know we have to be better. We have to find a way on Saturday to go out and get a result."