United progressed to the quarter-final, where they will face Brighton and Hove Albion at Old Trafford, after Romelu Lukaku's double sealed a 2-0 victory at John Smith's Stadium.
The major talking point occurred seconds before half-time, though, when Juan Mata's goal was ruled out for offside after a VAR referral despite conflicting views on whether the decision was correct.
Mourinho, whose side were winning 1-0 at the time, insists he is in favour of VAR when it comes to getting crucial calls right but feels match officials should have their say on whether the technology is given widespread use.
"The feeling is amazing when the truth comes, but there are problems, like what happened today," he told a news conference.
"Protocol says it needs to be a 'clear and obvious' situation and it was not clear or obvious. But we know it is experimental and I am speaking after a 2-0 victory.
"I think it should be the referees to decide. Do they want it, do they feel happy with it and do they want technological help? Or do they want to live with the mistakes they make as humans?"
Mourinho then joked his refusal to argue against the decision should stand him in good stead to be rewarded for his behaviour, something he has hinted at before this season.
"I am close to winning the best-behaved manager award this season. Nothing can make me lose that this season," he said.
"I'm happy we are in the quarter-final. I am happy to win the match after a defeat.
"The match was difficult because they approached the match differently than before because they didn't need to get a point for the league. They were offensive, they were dangerous, they pushed us to good defensive work."
There was a surprise early on Saturday when Paul Pogba was ruled out of the match through illness, just a day after Mourinho had hit out at suggestions of a falling-out with United's star midfielder.
"I was told by the doctors this morning that he wasn't coming," he added.
"I do not know when he will be back."