Rooney suffered a thigh injury towards the end of the first half and was replaced by Radamel Falcao before the start of the second period, while Shaw was struck in the face by an elbow from Crystal Palace midfielder James McArthur and had to be substituted off after 40 minutes.
However, van Gaal expects that both Rooney and Shaw should be fit for United's vital Premier League match against Arsenal on May 17.
"Shaw took an elbow and had a bloody nose, but he went to the hospital and I have already heard that he shall fly home with us so I don't think it is very bad," the Dutchman told MUTV. "Out of precaution, we took him off. Rooney had a dead leg so next week he is healthy and fit to play."
Despite the injuries, van Gaal was proud that his side went on to beat Crystal Palace and further cement their position in fourth place on the standings after Liverpool's match with Chelsea ended as a 1-1 draw.
"It was very bad because our team was out of balance," said van Gaal. "Phil Jones had to play as a left full-back. Rooney has a dead leg so I had to change things that were not in our favour at that time but, still these in circumstances, we fought until the end and we have beaten Crystal Palace."