Arsenal’s 1-1 draw with Brighton on Sunday, means the Gunners will all but finish outside the top four this season.
Unai Emery’s men needed to win their last home fixture of the season, to stand any chance going into the final round of games.
Pierre-Emerick Aubameyang gave the hosts an early lead, thanks to a controversial penalty.
Brighton were awarded their own spot kick in the second half and Glenn Murray made no mistakes from 12 yards.
The result leaves Arsenal with 67 points and means that Chelsea have sealed their place in the Champions League, having accrued 71 points in third place.
Spurs, who are in fourth place, have 70 points but a much better goals difference than their North London rivals.
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