Scott McTominay’s opening goal gave the hosts the advantage, but Villa were well the better team from that point on and didn’t have a chance not to level up.
Despite another difficult performance from United, Varane was still happy with the way the team defended themselves and the effort put in.
“It was a tough game,” admitted Varane. “We had to suffer a lot on the pitch but together and I liked the spirit of this match.
“We had the opportunity to score more goals. When it wasn’t possible to play higher on the pitch, we were compact and didn’t let them play easily.
“We had to be aggressive and suddenly it’s good. We are happy. We need more trust, we need to be together and I think we are on the right track.
Although the victory allows United to advance to the fourth round, where they will host Middlesbrough, it has not allayed concerns about the performances the club have produced this season.
There were reports of unrest in the locker room and some players not convinced by Ralf Rangnick, but Varane played down those distractions.
“We just need to focus on our work,” he said.
“We have to fight, we have to fight for our fans. That’s it.”