Ten-man Arsenal beat Everton 3-1 on Sunday to complete their Premier League campaign with a fifth successive win but there was no last-day reprieve for their top-four hopes.
First-half goals by Hector Bellerin and Alexis Sanchez and a stoppage-time effort by Aaron Ramsey sealed the win but Liverpool and Manchester City also won to leave Arsenal fifth, their lowest finish since Arsene Wenger arrived in 1996.
Arsenal will be missing from the Champions League for the first time in 20 years next season.
Bellerin put Arsenal ahead after eight minutes and although they lost Laurent Koscielny to a red card shortly afterwards Sanchez doubled their lead before halftime.
As news filtered through that Liverpool, whom Arsenal could have caught with a win if they had failed to beat Middlesbrough, were winning comfortably the early optimism evaporated.
LIVERPOOL 3 MIDDLESBROUGH 0
Liverpool ensured a return to the Champions League by beating relegated Middlesbrough on Sunday, although they will have to play in a qualifying round after finishing fourth in the Premier League, two points behind Manchester City.
Needing a win to make sure of a return to Europe’s premier club competition, Juergen Klopp’s side looked edgy early on but the tension was lifted just before halftime when Dutchman Georgino Wijnaldum scored from a clever pass by Roberto Firmino.
In the second half Philippe Coutinho curled in a direct free kick and Adam Lallana added a third goal.
Middlesbrough, who thought they should have had a penalty with the score at 0-0, finished as the lowest Premier League scorers this season with 27 goals.
WATFORD 0 MANCHESTER CITY 5
Manchester City made sure of third place in the Premier League when they romped to a 5-0 win at Watford on Sunday to ensure a Champions League berth for next season.
City were already 4-0 up at the break at Vicarage Road and finish the season with 78 points, ahead of Liverpool and Arsenal and behind Chelsea and Tottenham Hotspur.
Kompany opened the scoring with a fourth-minute header from a corner, followed by Sergio Aguero finishing off a counter attack set up by Kevin de Bruyne in the 23rd minute.
Ten minutes later Aguero netted his 33rd goal of the season at the end of another quick attack with Leroy Sane providing the decisive pass.
It was 4-0 in the 42nd minute as Fernandinho powered through the defence to score from close range with another Brazilian, Gabriel Jesus, adding a fifth goal 13 minutes after the break.
The match was the last for Watford manager Walter Mazzarri with his club finishing two places above the relegation standings after 38 games.
Summaries from the English premier league matches on Sunday
Swansea City 2 Jordan Ayew 71, Fernando Llorente 86
West Bromwich Albion 1 Jonny Evans 33
Halftime: 0-1;Attendance: 20,000
Burnley 1 Sam Vokes 23
West Ham United 2 Sofiane Feghouli 27, Andre Ayew 72
Halftime: 1-1;Attendance: 21,634
Chelsea 5 Willian 8, Eden Hazard 61, Pedro 77, Michy Batshuayi 90,90+2
Sunderland 1 Javier Manquillo 3
Halftime: 1-1;Attendance: 41,618
Hull City 1 Sam Clucas 66
Tottenham Hotspur 7 Harry Kane 11,13,72, Dele Alli 45+2, Victor Wanyama 69, Ben Davies 84, Toby Alderweireld 87
Halftime: 0-3;Attendance: 23,804
Leicester City 1 Jamie Vardy 51
Bournemouth 1 Junior Stanislas 1
Halftime: 0-1;Attendance: 32,000
Liverpool 3 Georginio Wijnaldum 45+1, Philippe Coutinho 51, Adam Lallana 56
Middlesbrough 0
Halftime: 1-0;Attendance: 53,191
Watford 0 Manchester City 5 Vincent Kompany 5, Sergio Aguero 23,36, Fernandinho 41, Gabriel Jesus 58
Halftime: 0-4;Attendance: 20,829
Manchester United 2 Josh Harrop 15, Paul Pogba 19
Crystal Palace 0
Halftime: 2-0;Attendance: 75,254
Arsenal 3 Hector Bellerin 8, Alexis Sanchez 27, Aaron Ramsey 90+1
Red Card: Laurent Koscielny 14
Everton 1 Romelu Lukaku 58pen
Halftime: 2-0;Attendance: 59,976
Southampton 0
Stoke City 1 Peter Crouch 58