Juan Mata bundled the ball home from close range just under 10 minutes into the second half to give United the lead at Old Trafford, before Marouane Fellaini doubled the advantage late on to put the Red Devils in command at the halfway stage of the tie.
However, Mourinho was unhappy with the team's first-half display and questioned why they celebrated breaking the deadlock when the match was still hanging in the balance.
"In cup ties every goal can be crucial and why celebrate when you have half an hour to play? I don't think so. I think there is no reason for a celebration with the first goal," he told Sky Sports News.
The second leg will take place at the KCOM Stadium on Thursday, January 26.