Arsenal did their part by defeating Everton 3-1 on Sunday, but the result needed to be coupled with Liverpool and/or Manchester City faltering to sneak into the top four and a Uefa Champions League spot. Neither club did.
Liverpool ensured a return to the Champions League by beating relegated Middlesbrough, although they will have to play in a qualifying round after finishing fourth, two points behind Manchester City.
City easily handled Watford, 5-0, to clinch third place.
Arsenal finished in fifth place with 75 points, only a point behind Liverpool’s 76.
The win over Everton was a fifth successive league win for hard-charging Arsenal, but it was ultimately not enough to break into the top four. The fifth-place showing is the lowest for the club since Arsene Wenger arrived in 1996. They will miss next year’s Champions League for the first time in 20 years.
That indignity will cost Arsenal an estimated £50 million (Dh 239.4 million; $65 million) in revenue and increase the pressure on Wenger, who has endured a miserable season filled with fan protests and calls for his resignation.
The Frenchman, who has yet to reveal if he will sign a new contract to extend his 21-year reign, could still finish the season with silverware as Arsenal face Chelsea in the FA Cup final next Saturday.
Chelsea assured the Premier League championship last week and Tottenham – who finished with a league-best plus-60 goal difference – were entrenched in second. Both clubs won again on Sunday’s final day of the 2016/17 season.
Harry Kane had a hat-trick as part of a seven-goal Spurs trouncing of Hull City. Kane finishes with 29 goals, good enough for his second straight golden boot.
Chelsea topped Sunderland 5-1, sending off the departing John Terry at 26 minutes (his shirt number) to a big ovation.
Sunday’s scores
• Arsenal 3-1 Everton
• Burnley 1-2 West Ham
• Chelsea 5-1 Sunderland
• Hull City 1-7 Tottenham
• Leicester City 1-1 Bournemouth
• Liverpool 3-0 Middlesbrough
• Manchester United 2-0 Crystal Palace
• Southampton 0-1 Stoke City
• Swansea City 2-1 West Brom
• Watford 0-5 Manchester City
*Agencies
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