Arsenal will play Europa League football next season after they failed to finish in the Premier League's top four for the first time since 1995.
A 3-1 win over Everton at the Emirates was not enough to secure qualification to European football's top competition as Liverpool finished a point ahead of the Londoners.
Jurgen Klopp's men knew a win over already-relegated Middlesbrough would guarantee them fourth place ahead of Sunday's matches.
The Anfield faithful were treated to a nervous display from the home side until Georginio Wijnaldum opened the scoring in the dying seconds of the first half.
The Reds went on to win 3-0 after further goals from Philippe Coutinho and Adam Lallana secured the victory.
Spurs striker Harry Kane won the Premier League's Golden Boot award for the second successive season after scoring a hat-trick in Tottenham's 7-1 win at Hull. It brought his tally for the season to 29.
John Terry received a guard of honour in the 26th minute at Stamford Bridge as the champions beat Sunderland 5-1 to finish their campaign with 93 points.
Sergio Aguero scores for Man City. Picture by: Steven Paston/PA Wire/PA Images
Manchester City secured third place with a comprehensive 5-0 win at Watford while Manchester United beat Crystal Palace 2-0 at Old Trafford.
Elsewhere, West Ham beat Burnley 2-1 at Turf Moor, Leicester drew 1-1 with Bournemouth, Stoke beat Southampton 1-0 at St. Mary's while Swansea won 2-1 at home against West Brom.
