Arsenal failed to qualify for the Champions League for the first time in 20 years despite a 3-1 win over Everton on the final day of the Premier League.
The Gunners began the day a point behind fourth-place Liverpool and were on course to displace the Reds when they took an eighth-minute lead.
But Liverpool, needing a win to ensure fourth, broke Middlesbrough resistance just before the break, and won 3-0.
Manchester City claimed third with a very easy 5-0 win at Watford.
Reaction from the final day of Premier League action
Europa League for the Gunners
Arsenal’s remarkable run of qualifying for the Champions League in 19 consecutive seasons came to its widely anticipated end on Sunday.
Hope grew among the home support when Hector Bellerin gave the Gunners an early lead and news filtered through that Liverpool were struggling against the relegated Teessiders.
But in first-half stoppage time Georginio Wijnaldum put the Reds ahead with a stunning strike, and Jurgen Klopp’s men eventually ran out comfortable winners.
The Reds will play in the Champions League for the first time since the 2014-15 season.
Liverpool suffered from early nerves at Anfield before Wijnaldum’s opener on the stroke of half-time eased the tension.
Philippe Coutinho added a second after the break with a free-kick, and Adam Lallana slotted in to make it 3-0.
Manchester City sealed third spot and automatic qualification for the Champions League group stage with an emphatic 5-0 win at Watford.
Pep Guardiola’s side required only a point to secure a top-four place, but instead of sitting back went about dismantling their opponents.
Sergio Aguero scored twice, after Vincent Kompany’s opener, with Fernandinho and Gabriel Jesus also getting on the scoresheet.