Pierre-Emerick Aubameyang scored twice as Arsenal beat Burnley at Turf Moor, but the Gunners failed to finish in the top four for the third successive season.
Unai Emery’s side secured fifth place meaning they go straight into the Europa League group stage next season.
And they can still qualify for the Champions League if they beat Chelsea in the Europa League final on 29 May in Baku.
Aubameyang, who scored a hat-trick on Thursday as Arsenal beat Valencia in the Europa League semi-finals, finished the season with 22 league goals.
That saw him tie for the Premier League Golden Boot with Liverpool duo Sadio Mane and Mohamed Salah.
Ben Mee gifted Aubameyang his first, miscontrolling a pass from Jack Cork to allow the Gabon striker to run in and slot past Tom Heaton on 52 minutes.
He then lashed in a volley from close range 11 minutes later and should have had a hat-trick, but with the goal at his mercy, he poked wide.
Burnley, who had already secured a fourth straight season in the Premier League, pulled one back as Ashley Barnes met Johann Berg Gudmundsson’s pass with a glancing header.
Arsenal’s 19-year-old forward Eddie Nketiah added a third with the last play of the game in the 95th minute as he poked the ball through Heaton’s legs.