Palace stole the points at the death when Dwight Gayle scored, meaning Villa have now lost four games in a row and no team in the Premier League has a worse home record.
They have scored only six goals in nine home games, all of which have come after half-time.
Although the hosts dominated possession, they created little in the way of real chances, with Andreas Weimann missing the two best openings.
Lambert, who confirmed Christian Benteke will not be fit for Saturday's match against Swansea at Villa Park, said: "It's tough to take.
"There was a lot of endeavour, a lot of hard work, but not much creativity and we were hit with a classic counter-attack.
"We had most of the game - Crystal Palace might have had the clear-cut chances, and the goal from their point of view was a terrific strike.
"The home form isn't good enough and lack of goals is contributing to not winning games. We have to stand up and be counted and try to go on that front foot. We have to create more when we have most of the ball.
"It was very tight. Crystal Palace got it right, they defended well and they defended deep. We needed that creativity or a goal to go in.
"We had decent chances with Andi's two but the important thing is, if you can't win it, make sure you don't lose it, and we got caught."
The home fans made their feelings clear at the end with boos ringing around Villa Park, and Lambert's side are now only three points clear of the relegation zone.
But the Scot insisted his side are not in the scrap to stay in the Premier League.
He said: "My job is to try to be as positive as I can, I'm not going to be downbeat. I've seen the table, like I do after every game. It's as tight as anything from midway right down."