Arsenal's manager Arsene Wenger watches from the touchline during the English Premier League football match against Everton at the Emirates Stadium in London on May 21, 2017Arsenal's manager Arsene Wenger watches from the touchline during the English Premier League football match against Everton at the Emirates Stadium in London on May 21, 2017 (AFP Photo/Justin TALLIS)
Liverpool's victory over Middlesbrough condemned Arsenal and manager Wenger to a fifth-place finish, making this the first season since 1996-97 to conclude with the club having not secured a place in Europe's elite competition.
Wenger's side will look to next weekend's FA Cup final against Chelsea for consolation, but they will have to do without Laurent Koscielny, sent off for a reckless early foul on Enner Valencia, and possibly Gabriel.
Gabriel was stretchered off in the second half at the Emirates with an apparent knee injury and with Shkodran Mustafi absent here due to illness, it leaves Wenger facing a selection crisis in defence.
Arsenal prevailed courtesy of goals from Hector Bellerin, Alexis Sanchez and Aaron Ramsey, with Romelu Lukaku replying from the penalty spot for Everton to take his tally for the campaign to 25 goals.
Despite a seventh win in eight league games, it added up to a disappointing afternoon for Wenger, whose Arsenal future remains undecided pending a board meeting scheduled to take place after the cup final.
It is thought failure to qualify for the Champions League will cost Arsenal around £50 million ($65 million, 58 million euros).
The topic of Wenger's future divides Arsenal's fans, but they reserved their fiercest ire for American majority shareholder Stan Kroenke, dubbed "Silent Stan", chanting: "Stan Kroenke, get out of our club!"
Arsenal had been quick to settle the home fans' nerves as they took the lead in the eighth minute, but it was no thanks to Danny Welbeck.
Presented with an open goal by Mesut Ozil's low cross from the left, the former Manchester United striker somehow contrived to let the ball run underneath his foot, but Bellerin followed up to score.
Arsenal were in complete control, only for Koscielny's moment of madness to give Everton hope.
- Everton statuesque -
Seeking to halt Valencia as he sped down the Everton right, the Frenchman launched himself into a full-bodied lunge that sent his opponent flying and yielded an immediate red card from referee Michael Oliver.
Everton manager Ronald Koeman looked to exploit the situation by sending on Ross Barkley for Tom Davies, but it was Arsenal who struck next in the 27th minute.
Sanchez's shot from range was deflected into the path of Welbeck, who drew Everton goalkeeper Joel Robles from his line and, with the visiting defence statuesque, teed up Sanchez to tap in his 24th goal of the campaign.
Sanchez also saw a free-kick parried by Robles, but as half-time neared, Everton's numerical advantage began to tell as Arsenal goalkeeper Petr Cech increasingly found himself in the firing line.
He boxed away a deflected cross by Kevin Mirallas, turned away an Idrissa Gueye drive, athletically tipped over a Lukaku header and fielded a drilled effort from Valencia.
Lukaku, meanwhile, saw an effort diverted wide by Gabriel after being set up by Barkley.
When Arsenal re-emerged for the second half, it was in the knowledge that Georginio Wijnaldum had put Liverpool ahead against Middlesbrough on the stroke of half-time at Anfield.
They started brightly, Robles saving in quick succession from Welbeck and Ozil, only to lose a second centre-back of the afternoon when Gabriel was carried off after hurting himself in a challenge with Valencia.
It meant Arsenal finished the game with club captain Per Mertesacker -- making his first appearance of the season -- and 21-year-old Rob Holding in central defence.
Lukaku halved the arrears in the 58th minute, steering a penalty into the bottom-left coner after Holding was adjudged to have handled Leighton Baines's cross.
Everton, already assured of seventh place and a Europa League berth, finished strongly, but Ramsey had the last word, arcing a delightful shot into the top-right corner in the final minute.