Argentina international Rojo, who endured a brief spell on the sidelines earlier this season after dislocating his shoulder in November, was expected to face Brendan Rodgers' men at Old Trafford.
However, he picked up an injury in training before the game and was replaced by Phil Jones - who himself returned from a prolonged absence due to a shin problem.
"Rojo was good. Only yesterday he was in a training session and he got injured and then I had to change my line-up again," Van Gaal said. "It's what I have to do every week.
"It's more easy when all the players are fit and you can select the best player you think [should play], but we cannot do that at the moment."
"The most important thing is our philosophy, and when you stick by your philosophy and you follow the principles of that philosophy, every player can do that, because every player has played already in that philosophy.
"It's amazing that we can do that because it's not so easy."
