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 to a 1-1 draw at home to lowly Brighton.
With Tottenham losing on Saturday and Manchester United only managing a draw at Huddersfield earlier in the day, a win for Unai Emery's side would have taken them to within a point of Spurs in fourth spot.
Instead they head into the final day against Burnley three points adrift of Spurs and with a significantly inferior goal difference after Brighton toasted their survival with a hard-earned point.
Leaders Liverpool and Manchester City have already sealed the top two spots and Arsenal can no longer catch third-placed Chelsea, who are on 71 points, four points ahead of them.
Arsenal, however, can reach the Champions League by winning the Europa League and they are well-placed to make the final, with the Gunners 3-1 up after the home leg of their semi-final against Valencia.
A disappointed Emery, in his first season at the Emirates after replacing long-serving boss Arsene Wenger, turned his thoughts to the Europa League tie in Spain after the match.
"We deserved to win but we know they are defensively very strong and played very well," the Spanish boss told Sky Sports.
"We fight and try to win each match in the Premier League but every match is difficult and today is an example of that," he added.
"We knew it is going to be difficult but our focus is now the Europa League," he told the BBC. "We have the opportunity in the Europa League to do something important and we will try and do that."
Emery made five changes for Arsenal's final Premier League home game, juggling the club's league ambitions with Thursday's second leg in Valencia, including recalls for Nacho Monreal, Lucas Torreira and Henrikh Mkhitaryan.
Arsenal were impressive in the opening stages at the Emirates and were awarded a contentious early penalty, referee Anthony Taylor pointing to the spot after he adjudged Alireza Jahanbakhsh to have tripped Monreal.
Pierre-Emerick Aubameyang converted the spot-kick in the ninth minute for his 20th Premier League goal of the campaign.
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 to extending Arsenal's lead shortly before half-time.
Brighton levelled from the spot in the 61st minute. Solly March went down after a foul from Granit Xhaka and Glenn Murray found the net from the resulting penalty.
Aubameyang missed a golden chance to restore Arsenal's lead as the home side poured forward and Brighton goalkeeper Mat 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.
The performance from the home side saw plenty of fans head for an early exit, with many of those who remained jeering at full-time despite the post-match lap of honour and farewells for the retiring Petr Cech and Juventus-bound Aaron Ramsey.