Arsenal's chances of qualifying for the Champions League via a top-four finish in the Premier League were all but snuffed out on Sunday as they were held 1-1 by lowly Brighton.
The draw leaves Unai Emery's men in fifth spot, three points behind north London rivals Tottenham, who have a far superior goal difference, and means they can no longer catch Chelsea, who have 71 points.
Leaders Liverpool and Manchester City have already sealed the top two spots ahead of the final round of Premier League fixtures next weekend.
Arsenal can also reach the Champions League by winning the Europa League and they are in a strong position to reach the final, 3-1 up after the home leg of their semi-final against Valencia.
Emery made five changes for their final home game, juggling the club's league ambitions with Thursday's second leg in Valencia, including recalls for Nacho Monreal, Lucas Torreira and Mkhitaryan.
Arsenal were impressive in the early stages at the Emirates and Pierre-Emerick Aubameyang struck from the penalty spot in the ninth minute after Monreal was brought down in the area by Alireza Jahanbakhsh.
The visitors, whose Premier League survival was assured when Cardiff lost at home to Crystal Palace on Saturday, came back strongly, putting pressure on a nervy home side but Aubameyang went close shortly before half-time.
Brighton levelled from a disputed penalty in the 61st minute.
Solly March went down under minimal contact from Granit Xhaka and Glenn Murray found the net from the resulting spot-kick.
Aubameyang missed a golden chance to restore Arsenal's lead as the home side poured forward and Ryan blocked an effort from Alexandre Lacazette.
Emery then made a triple substitution, throwing on Matteo Guendouzi, Alex Iwobi and Sead Kolasinac for Mkhitaryan, Xhaka and Lichtsteiner but despite frantic late Arsenal pressure, they could not find a winner.
They have a goal difference of +20, compared to Tottenham's +28, meaning Spurs, who host Everton next week, are almost assured of finishing the season in fourth spot.
Arsenal travel to face Burnley in their final league game.
Earlier, Manchester United's hopes of Champions League football next season were ended after an embarrassing 1-1 draw at already relegated Huddersfield.
United have now won just two of their past 11 games in all competitions as Huddersfield ended a run of eight straight defeats despite goalkeeper Jonas Lossl's error handing the visitors an early lead through Scott McTominay.
Terrible defending from Ole Gunnar Solskjaer's men gave the Terriers something to celebrate in their final home game before heading down to the Championship as Isaac Mbenza levelled on the hour mark.