Liverpool and Chelsea secured the final two Champions League qualification spots on a thrilling last day of the Premier League season, with Leicester missing out in the three-way fight for a top-four finish on Sunday.
Chelsea's 2-1 defeat at Aston Villa didn't prove critical because Leicester conceded three late goals to lose 4-2 at home to Tottenham and stay in fifth place.
Liverpool beat Crystal Palace 2-0 and jumped into third place, two points above fourth-place Chelsea.
Leicester also missed out on Champions League qualification by losing on the final day of last season.
West Ham beat Southampton 3-0 to finish in sixth place to qualify for the Europa League and Tottenham's win at Leicester ensured the team got into the new Europa Conference League.
Sergio Aguero marked his final Premier League game for Manchester City by scoring twice as a substitute in the champions' 5-0 win against Everton.
Harry Kane finished as top scorer on 23 goals — one ahead of Liverpool's Mohamed Salah — after scoring at Leicester.