FORMER Arsenal manager Unai Emery, who had won this title three times with Sevilla, oversaw a tough night for United.
But in truth, Solskjaer’s men had themselves to blame for not finishing the game off during the second half.
Villarreal took a surprise lead and if that was not bad enough for United’s Liverpool-hating fans, the scorer was Gerard.
Edinson Cavani levelled on 55 minutes after dashing back from an offside position to score, although it was still a close call and needed a VAR check.
Yet the winner in 120 minutes never came and there will be questions rightly asked about Solskjaer’s game-management.
The Norwegian felt no need to introduce any subs until well into extra-time, while Emery made five changes in the 90 minutes.
United’s first change came in the 100th minute with midfielder Fred replacing attacker Mason Greenwood, who had a decent game.
It was a conservative change but Villarreal, who finished seventh in LaLiga, were just beginning to take control.
Generally, though, this was a scrappy performance from United despite all their possession. And for periods it was hard to watch.
Solskjaer was furious through a sloppy first-half display which saw his side rarely threaten.
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The second period was much better but, as you would expect with only a few fans inside the ground, the atmosphere remained a bit weird for a European final.
In a gate of more than 9,000, there were 2,000 tickets for each club with the rest going to locals.
But throughout the day, and also inside the stadium, it felt like there were more Spanish than English supporters — and they were certainly the noisier.
Of those wearing Manchester United shirts, many were Polish.
It was an attack-minded side from Solskjaer, with Fred making way for Paul Pogba to start in central midfield and Greenwood — who squeezed into Gareth Southgate’s 33-man provisional England squad — starting out wide.
United’s players took the knee before kick-off — Villarreal’s did not — and they started off on the front foot but without any major success.
Scott McTominay and Luke Shaw screwed shots wide without troubling Villarreal keeper Geronimo Rulli
Juan Foyth, on loan from Spurs, suffered a bloody facial injury that required a bandage and a fresh yellow shirt after Pogba fell on his head.
Sub Yeremi Pino had a goalbound shot deflected for a corner by McTominay.
Yet the Spaniards were perfectly happy to sit back and offered virtually nothing going forward.
So it was a surprise when they struck the first blow thanks to a free-kick needlessly conceded by Cavani, although both De Gea and Pogba were guilty of losing possession before that.
Dani Parejo’s delivery to the far post was outstanding and Gerard Moreno peeled away from Luke Shaw and found space between Victor Lindelof and Eric Bailly before prodding the ball past De Gea from just outside the six-yard box.
Incredibly, it was the first goal between these two teams after four successive goalless draws.
United’s bewildered defenders looked at each other.
Harry Maguire, not fit enough to start, was on the bench knowing that he would have got his head to the delivery.
Going behind failed to spark United into action.
Their play was low-tempo and directionless and Rashford made constant mistakes.
United’s best chance of the opening 45 minutes came through Villarreal defender Raul Albiol, as he sent Greenwood’s cross back towards the goal but fortunately, it was straight at keeper Rulli.
There was chaos at the start of the second half as Villarreal attempted to score from a goal-mouth scramble after Bailly.
United got away with it — then failed to land a penalty from VAR after Greenwood was kicked by Alfonso Pedraza.
But their luck soon changed. Shaw’s corner was headed clear by Albiol but only to Rashford, and while his volley was blocked, the ball fell perfectly for Cavani to drive a shot under Rulli.
After an agonising wait for another VAR check for offside on Cavani, French referee Clement Turpin pointed to the centre circle.
Rashford delivered a contender for miss of the season from eight yards — so he was probably thankful it would have been ruled offside had he scored.
Cavani had a header blocked but with Villarreal defending for their lives, a United winner looked increasingly likely but did not materialise.
Villarreal improved in extra-time and while they are an unremarkable team, they got over the line in a dramatic penalty shootout.
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