Arsenal have failed to qualify for the Champions League for the first time since Arsene Wenger took over as manager in 1996.
The Gunners beat Everton 3-1 on the final day of the Premier League season at Emirates Stadium, despite having captain Laurent Koscielny sent off, but it was not enough to lift them into the top four.
Manchester City's 5-0 win at Watford and Liverpool's 3-0 victory over Middlesbrough ensured they claimed the final two Champions League spots, behind champions Chelsea and second-place Tottenham.
Next season will be Arsenal's first outside Europe's top competition since 1996-97, which was Wenger's first in English football, and they must instead take part in the Europa League.
Protests against Wenger are likely to increase following the disappointment, with a number of fans having called on the 67-year-old not to be given a contract extension following frustrating results this term.
Wenger said he will make an announcement on his future following the FA Cup final on May 27.