Marcos Rojo suffered a dislocated shoulder during yesterday's derby.
Rojo had to be taken off early in the second half - after Chris Smalling had earlier been sent off - to leave United seeing out the game with Michael Carrick and Paddy McNair in central defence.
A frustrated Van Gaal confirmed Rojo's injury last night saying: "The shoulder is out so you never know how long that is out. You never know how long that will take I have to wait until Monday, I think, but he shall not play against Crystal Palace I think."
With Smalling and Rojo set to be out for next week's clash against Palace at Old Trafford, Van Gaal may be forced to field a patched up backline from the start but he insists they will manage.
"We have still 11 players to play and also very good players so I don't cry for that but it is sometimes difficult to select the best team - but I think I can manage that," he added. "And we are close, you can see it every week, but we need more points. When I see the fans they are applauding after the game so they see also the boys are willing to give everything."