N'Golo Kante's ripping strike in the second half secured the Blues a 1-0 victory, but the holders were already a man short after Herrera collected a second yellow card for a foul on Eden Hazard in the 35th minute.
United have failed to win any of the four games in which Oliver has controlled them this season. The official awarded United's opponents penalties in draws with Everton and Liverpool, as well as the September defeat at Watford.
And Mourinho claimed post-match that Oliver had not been consistent in dishing out punishments for offences similar to Herrera's throughout the match.
"I just want to say that I'm really proud of my players, proud of the Manchester United fans," he told the BBC.
"We have a very important match on Thursday [against Rostov in the Europa League] and I want to try to rest a little bit to prepare the team the best we can for Thursday's match and that's the most important thing.
"We can analyse different perspectives, everyone can do it in a different way but I think we all watched the match until the red card and after the red card.
"Then we can compare the decisions of these two yellow cards in this case the second yellow card with other ones that weren't given.
"But I don't want to go in that direction. This season Mr Michael Oliver, he is a referee with fantastic potential, but with Manchester United we are a bit unlucky.
"In four matches, three penalties and one red card, and [the red card was] in such an early moment of the game.
"But, again, I cannot change that but I can try to interfere in Thursday's match."