The two clubs meet on Saturday afternoon with Palace currently just three points adrift of safety and four points behind Brighton, who sit in 14th place in the standings.
Van Aanholt has acknowledged that things are "tight" in the bottom half of the table, but says that can change with a positive result at Selhurst Park.
The 27-year-old told the Daily Mail: "It's very important to get the win on Saturday, not just for the fans but for us as well. Winning the match pushes us up the table and puts us just one point behind Brighton with four games to go.
"At the minute, it's very tight at the bottom half off the table, but everything can change with one game. We have to look at ourselves and perform to a high standard, like we have been doing these last couple of months."