Manchester United beat Brighton & Hove Albion 2-0 at the Amex on the final matchday of the campaign but still finished eighth in the Premier League table.
Diogo Dalot made the breakthrough in the 73rd minute, with the Portugal international impressively finding the back of the net with a calm finish after a long pass from Casemiro, before Rasmus Hojlund came off the bench to add a late second for the visitors.
Newcastle United, though, secured seventh in the table courtesy of their 4-2 victory at Brentford.
Eighth represents Man United's worst-ever performance in the Premier League, and they are now relying on beating Manchester City in next weekend's FA Cup final to qualify for Europe next season.
Indeed, should Erik ten Hag's side overcome Man City, they would secure a spot in the 2024-25 Europa League group stage, but a loss would leave them without any form of European football.
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Man United must win FA Cup final to qualify for Europe
It remains to be seen whether this was Ten Hag's final league game in charge of Man United, but it was certainly the final time that Roberto De Zerbi will manage Brighton, with the Italian leaving this summer.
The hosts shaded Sunday's contest at the Amex for long spells but were unable to find the back of the net, and they conceded twice in the latter stages to suffer their 14th league defeat of the campaign.
Brighton had a sight of goal inside the opening five minutes, but Adam Webster's header from a corner was always missing the target, with Man United giving an early warning.
Alejandro Garnacho was then almost in down the other end, only for Jakub Moder to make a wonderful challenge, preventing the Argentina international from breaking through on goal.
Man United's first serious chance arrived in the 26th minute, with Bruno Fernandes setting up Scott McTominay, but the Scotland international fired his effort over the crossbar.
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Man United finish eight points off the top four
Brighton were next to come close, with Joao Pedro sending one wide of the far post after smart work from Adam Lallana on what was his final appearance for the Seagulls.
It was a first period that had a final-day feeling for long spells; Brighton had 10 shots in the opening 45 minutes, though, while Man United only managed two, and the home side also had more of the possession (58%).
Casemiro cleared one off the line early in the second period, with Pedro coming close again, and Brighton were certainly the team forcing the issue at the Amex.
However, Dalot sent Man United ahead in the 74th minute, with the full-back finding the back of the net after a long pass from Casemiro had caused Brighton's defence problems, before Hojlund netted his 10th league goal of the campaign late on to secure all the points for Ten Hag's side.
Raphael Varane was introduced in the 69th minute for his final league appearance in a Man United shirt, and the result will certainly have boosted confidence in the Red Devils camp ahead of what is shaping up to be a fascinating clash against Man City at Wembley next weekend.
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