N’Golo Kante scored the only goal in the second half, as the Blues marched into the semi-finals where they face London rivals, Tottenham Hotspur.
United were reduced to 10 men in the first half, after referee Michael Oliver showed Ander Herrera two yellow cards.
When asked after the game to comment on the sending off, Mourinho said: “I don’t speak. I am proud of my players and United fans.
“Everybody will analyse different perspectives in a different way but we all watched the match and saw the red card and after the red card.
“We can compare the yellow card with other ones which were not given but i don’t want to go in that direction.
“Mr Michael Oliver is a referee with fantastic potential.
“Manchester United have been unlucky. I cannot change that.”
Mourinho will now turn his attentions to their Europa League fixture against FC Rostov this Thursday at Old Trafford. The first leg ended 1-1.