Brighton were forced to settle for a place in the Conference League after Manchester United marked Michael Carrick's first match as permanent manager with a thumping 3-0 success and a record for Bruno Fernandes.
The Seagulls began the final day in pole position for a Europa League place but with the potential to qualify for any of the three European competitions, or miss out altogether.
United captain Fernandes set up Patrick Dorgu's opener to claim the outright Premier League assist record with a tally of 21, before Bryan Mbeumo doubled the lead in the closing minutes of the first half.
Fernandes, whose assist moved him clear of Kevin De Bruyne and Thierry Henry's previous record, further celebrated being crowned Premier League player of the season by scoring the visitors' third early in the second period.
Brighton offered little during a deflating end to the season and must be content with playing in European club football's tertiary competition next term, having slipped to eighth place.
Carrick, meanwhile, will turn his attention to bolstering his squad for Champions League football after reviving United's fortunes with 12 wins from 17 top-flight games following his appointment.
The former Red Devils midfielder made three changes following last weekend's 3-2 win over Nottingham Forest and watched his side take control of the contest in the latter stages of a largely uneventful first half.
Seagulls head coach Fabian Hurzeler responded to the smattering of boos which greeted the half time whistle by introducing winger Yankuba Minteh in place of Maxim De Cuyper for the second period.
However, realistic hopes of an Albion fightback were extinguished within three minutes of the restart.
Following a swift United counter-attack, Fernandes thumped a low shot into the bottom left corner after being slipped in by Dorgu, with the goal eventually given after VAR overturned an offside decision.
Goalkeeper Bart Verbruggen produced smart stops to twice deny Dorgu his second, either side of pushing away a powerful effort from Diallo.
Diego Gomez dragged wide and substitute Solly March stung the palms of Senne Lammens as Brighton sought a response.
Yet United were not unduly tested as they signed off in style, despite dropping out of the second Europa League spot.
There were euphoric scenes at full time as Brighton's players and fans revelled in securing European football for only the second time in the club's history.