Van Dijk admits Palace deserved the win, but with a Champions League trip to Galatasaray on Tuesday, he insists there's no reason for panic.
He said: "The biggest challenge now is to stay calm. I have mentioned it many times: never get too high or too low. Just work and don't listen to the outside world too much.
"You know when you can do better and everyone knew that.
"We are disappointed in our performance. Disappointed in the loss, but especially the way we went about it. I think if we got a draw, then we took already one point too many.
"I don't think there is any reason to worry, but we have to improve pretty quickly because obviously we play in Turkey on Tuesday. We have a very difficult game there as well, so we have to be ready."
Van Dijk also said: "It was the basics that we didn't do well. Sometimes you can have these days. Hopefully this is the only day this season that we do that.
"There is a reason Palace were 17, now 18, games unbeaten. They are very difficult to break down, very disciplined, they defend deep and they don't mind that, and they have the quality on the break to hurt you.
"But it started all with ourselves. We were sloppy in possession, didn't win our second ball fight, and we created momentum for them. They could have been three or four up by half-time.
"We are lucky that we have, in my opinion, the best goalkeeper in the world to save us."