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United had a host of chances after the break but found Sevilla goalkeeper Bono in superb form.
They were made to pay for their profligacy in front of goal when Sevilla substitute Luuk de Jong scored from close range with 12 minutes left to send the Spanish side through and ensure United reached a series of grim milestones.
They have now been eliminated from European competition by Spanish opposition for the third consecutive campaign, also losing to Sevilla in the Champions League last 16 in 2017-18 and Barcelona in the 2018-19 Champions League quarter-finals.
It is the third semi-final defeat for United this season, having lost to Manchester City in the last four of the Carabao Cup in January and to Chelsea in last month’s FA Cup semi-final at Wembley. United are now thefirst team to ever lose both domestic cup semi-finals and a European semi-final in the same season.
Defeat against Sevilla alsomeans the Red Devils finish without a major trophy for a third season in a row – their longest run since four successive seasons without a major trophy between 1985 and 1989.
When assessing this latest defeat, Solskjaer will likely rue a lack of cutting edge in front of goal.
His side managed 46 shots across the Sevilla game and their semi-final win against FC Copenhagen, with 21 of those hitting the target, but they only managed to score two penalties.
Victory for Sevilla meanwhile continued their remarkable run in this competition. The Spanish side have now reached their sixth UEFA Cup/Europa League final, at least two more times than any other side in the history of the competition.