Shaw appeared to take a blow to the face from James McArthur and looked shaky when he went to ground to receive treatment. The fledgling left-back, making his 20th appearance of the season, was then replaced by Jonny Evans on 40 minutes.
Rooney sustained a couple of heavy knocks to his left thigh and was hobbling at the end of the first half. The captain reappeared on the pitch at the break, attempted a quick warm-up but it was seemingly decided he wasn't fit and was replaced by Radamel Falcao.
"It was very bad because our team was out of balance," van Gaal told MUTV at Selhurst Park. "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.
"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. Out of precaution, we took him off. Rooney had a dead leg so next week he is healthy and fit to play."