The hosts were booed off the pitch on Thursday after Dwight Gayle's late strike earned Crystal Palace a 1-0 victory.
It was Villa's fourth straight defeat in the Barclays Premier League and the fifth time in six matches that they have failed to score at home.
They do not have to wait long to try again, with Swansea the visitors on Saturday.
Hopes were high for a better season at Villa Park after they got out of trouble with a strong finish to last term and began well this time, but those have faded.
Lambert said: "We don't want to dwell on it because we've got a quick turn around and we have to go again on Saturday. You have to pick yourself up and meet the challenge. There's no point in wilting.
"The way you bounce back is by winning. That's what we have to do and try to give the supporters something to go with. The support's there - this club have always had the support and always will do. It's important that everybody sticks together.
"The fans vent their frustration in the same way they get behind you when you're winning. You have to be big enough to take it and you have to see it through. You can't run away from it, it's there.
"It's the same group of lads that went on that run last year so I don't have a problem with that."
The Villa boos were almost drowned out by the delighted cheers of the Palace fans, and boss Tony Pulis admitted frustrating the home fans had been part of his tactics.
"We knew if we could keep them quiet the crowd might get a bit restless, and that's what we managed to do," he said.
Pulis said this week he was not sure Gayle was ready for Premier League football but he gave the 23-year-old record signing the final 18 minutes at Villa Park to stake his claim.
And with three minutes of injury time ticking down, Gayle picked up the ball on the left, beat Fabian Delph and curled a superb shot into the top corner.
Pulis said: "It's a fantastic strike. He can do that and there was no one more pleased than myself to see it go in.
"It's the same with Johnny Parr at left-back, I haven't seen a lot of certain players. I'm a manager that picks a team and, if you're in that team, it's more difficult to get out of the team, that's the way I've always managed.
"Sometimes for the people who haven't started, it's difficult to get that run of games, especially if the team does all right. Apart from the Newcastle game, the team has done exceptionally well."