Dwight Gayle's superb late goal secured victory for Palace on Thursday and left Villa, who have won just two home league games out of nine this season, a mere three points above the Premier League relegation zone.
Lambert's men have the chance to make immediate amends when Swansea City visit Villa Park on Saturday.
The Scot has urged his team to bounce back and give their supporters reason for cheer.
"We have no time to dwell on it (the defeat to Palace) because there's a quick turnaround. We have to go again on Saturday," he said.
"It's the old cliche but you have to pick yourselves up. You have to meet the challenge.
"There's no point wilting. I am disappointed. But you pick yourself up and meet that challenge."
Asked about Villa's dismal home form, he added: "It isn't good enough. You have to turn it around.
"There's no magic formula. There's more pressure because of the size of crowd but you should overcome that. That should be a given. The crowd are right on your side.
"You have to stand up and be counted. We have to get on the front foot. We have to create more.
"There shouldn't be too much pressure because you've got 40,000 behind you every time.
"We have to give them something to go with. You can't be critical of the fans here because they have backed us all the way.
"It's important everyone sticks together. I understand their (the fans') frustration. You have to be big enough to take it. You have to see it through. You can't run away from it. It's there."
Lambert takes heart from Villa's form in pulling away from trouble last season.
"The team is big enough to take it. It's more or less the same group of lads who went on that run last time," he added.
"My job is to be as positive as I can. That's my job. I am not going to be downbeat.
"You have to get them going again for Saturday."
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