In fact, Gerard Moreno had given Unai Emery’s side the lead just before the half-hour mark when he lost his marker to put Dani Parejo’s free-kick past David De Gea.
Though Edinson Cavani equalised for the Red Devils 10 minutes into the second-half, United struggled to break down their Spanish opponents in Gdansk.
That failure to score sent the game to a penalty shootout, from which Villarreal emerged victorious after both sides put on a spot-kick masterclass.
De Gea missed the crucial penalty which saw United lose and hand Emery’s men their first ever major trophy.
It meant that the season ended on a disappointing note for Solskjaer and United, after the club had made clear progress this campaign.
Several areas of the squad are expected to be upgraded when the window opens, with a new striker and a new winger believed to be on United’s shopping list.
Despite signing Edinson Cavani up to a new deal, a second goalscorer is needed after Cavani spent spells on the sidelines over the course of the campaign.
Question marks also remain over the right position for Mason Greenwood long-term, though he has impressed on the wing.
But the teenager has said that he sees himself as a main striker going forward, potentially opening up a spot on the right.
Who should Manchester United sign this summer? Comment below.
Neither Anthony Martial nor Dan James have shown the quality desired of a first-team regular, with the Red Devils eyeing a move for Jadon Sancho.
O’Shea and Solskjaer played together for eight years at Old Trafford, helping the club to win four Premier League titles and the FA Cup.
And the Irishman believes that his former team-mate Solskjaer is doing the right thing by seeking to upgrade his attacking options when the summer transfer window opens.
“He will be questioning himself. I think the whole team will be questioning themselves with that attacking talent on threat,” the former Republic of Ireland defender told talkSPORT.
“I think Ole picked that team thinking there’s going to be no issues we’re going to win that game with that attacking talent and that’s where probably they’ll look at in the summer for reinforcements.
“It does need improvement – they’ve always said that – going unbeaten away in the Premier League is no mean feat but they need more.
“It was a disappointing result and they’ll have to face up to the reality of that.”