Villa are hovering just four points above the Premier League's relegation zone after Saturday's loss, which came after defeats against Stoke City, Manchester United and Fulham.
Jason Puncheon scored the only goal of the game with 14 minutes to play, setting up a crucial clash against Southampton at Villa Park next week.
"We've got to go into our next game and win it," Lambert said.
"You can't let (the defeat) manifest. We've got to stop the sequence of losing four games. That's got to stop.
"You can't let your head go down. You've got to keep going. We've got to go and win the next game. I told the lads that.
"There are teams a lot worse off than ourselves. You look at the table, it's really congested. We've got to win our next game.
"You have to get over that finishing line as quickly as you can.
"We need the fans against Southampton. There's no doubt. They will come in their numbers to watch us and get right behind us."
Lambert believes there was very little between the two sides at Selhurst Park and felt Villa did not take their chances.
"They've been playing really well so I knew coming here was a difficult game," he said.
"I thought it was an even game, there wasn't much in it. I thought it could have gone either way.
"They took their chance and (Crystal Palace goalkeeper Julian) Speroni's made a great save from Andi (Weimann).
"If we had got a point it would have been a good result. But to lose a goal in that way was disappointing."
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