Villa had gone into the break leading thanks to Bertrand Traore’s stunning goal, only for Bruno Fernandes to level from the penalty spot and Mason Greenwood to add a second shortly afterwards.

Substitute Edinson Cavani wrapped up a 3-1 victory that left second-placed United on the brink of back-to-back top-four finishes for the first time since Sir Alex Ferguson retired, and it was rubberstamped later in the afternoon when West Ham lost at home to Everton.

“I believe in the boys and I think they believe in themselves,” United boss Solskjaer said. “We know that sometimes coming back from Europe is difficult and there wasn’t a lot wrong with the first half either.

“We didn’t have the margins. They scored and we didn’t. I thought we created the biggest chances, opportunities, but they scored a very good goal.

“Then it was just about trusting ourselves again. We have done it so many times and it’s about ‘here we go again, boys, just keep moving the ball quicker’. That was one of the messages.

“The players are learning, a developing group as a whole, they’re getting better. The spirit, the camaraderie, they back each other. There’s competition for places so I’m very happy that we’ve done that twice now (reaching the top four).

“Of course we’ve got a final to look forward to – hopefully that will be with Harry Maguire. I don’t know. We’ve got to check him. It might be a few weeks, might be a couple of days, who knows?

“Hopefully it won’t be too bad but I’m not a doctor. We’ve got to check him and scan him tomorrow.

“It was his ankle, lower leg. I think the boy landed on top of him, so twisted his ankle and got a knock.”

Maguire had been on the cusp of becoming the first outfield player in United’s history to complete 72 consecutive Premier League matches before limping off late in the second half.

The skipper is a doubt for this week’s matches against Leicester and Liverpool, which could see the Red Devils move within four points of leaders Manchester City if they triumph in both.

“It is what it is,” Solskjaer said. “It’s very unlikely obviously that they (City) won’t get the points they need but we just have to do our jobs as well as we can.

“Tuesday will be a difficult game, Thursday’s another difficult game, so for these boys I don’t put it beyond them. They can go again, which we’ve shown so many times.”

While United celebrated, Dean Smith was left fuming with the officiating at Villa Park and Stockley Park.

The Villa boss was perplexed by the decision to award the match-levelling spot-kick for a Douglas Luiz challenge on Paul Pogba, before referee Chris Kavanagh handed Ollie Watkins a second booking for an apparent dive.

“I’m pleased obviously with the first-half performance but disappointed with probably our mentality and reaction to that penalty and the goal,” said Smith, who believes it is “pathetic” they cannot appeal Watkins’ sending-off.

“They started the second half better than us and for 20 minutes that was the problem in terms of the result for ourselves.

“The penalty for me is very, very soft. The red card for Ollie Watkins is very, very soft and probably the word I’d use is ‘confused’ because I don’t know where we are any more in terms of decisions like that.

“We saw Raheem Sterling’s yesterday and it wasn’t given and that’s with our so-called technology and VAR looking at it. Today’s was, so I think we’re all left scratching our heads.

“Maybe I need to coach my players like Keinan Davis at the end at 2-1, he goes through and maybe he should stick the brakes on and wait for the touch and go down to earn a penalty.

“I’m fed up with talking about penalty decisions against Manchester United. We’ve had three dubious ones in the three games against them.”