Arsenal can no longer catch third-placed Chelsea, who are on 71 points, four points ahead of them
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.
Man Utd's hopes ended
Manchester United's hopes of Champions League football next season were ended after an embarrassing 1-1 draw at already-relegated Huddersfield on Sunday.
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.
Chelsea's 3-0 victory over Watford means United fall four points outside the top four with just one game of the season to go.
And failure to beat statistically one of the worst teams ever to play in the Premier League will see further questions raised over the decision to hand Solskjaer a three-year contract in March.
The Norwegian has bemoaned United's lack of goals of late and recalled Alexis Sanchez to his starting line-up for the first time in two months in the search for more firepower.
But the Chilean again failed to live up to his status as the club's highest earner before limping off just before the hour mark.
Instead the visitors had to rely on Huddersfield for a helping hand as McTominay's strike from the edge of the box went straight through Lossl's legs after just eight minutes.
United quickly got the game restarted as they sought more goals to improve their inferior goal difference compared to their rivals for a top-four finish.
However, even against a Huddersfield side that previously registered just 14 points all season, United could not press home their advantage.
Juan Mata curled inches wide after some neat interplay between Marcus Rashford and Paul Pogba before Pogba also saw a looping header come back off the crossbar.
Solskjaer had kept faith with David de Gea in goal despite three high-profile errors leading to goals in his previous four games.
Huddersfield did not even test De Gea's nerve until five minutes before the break when Karlan Grant broke clear after an errant clearance from Phil Jones.
However, De Gea spread himself well to block a weak finish with his legs.
Huddersfield had only scored nine goals at home all season, but one hopeful punt from Lossl cut United open for the equaliser on the hour mark.
Luke Shaw failed to cut out the Danish goalkeeper's clearance and allowed Mbenza a clear run on goal to slot between De Gea's legs.
A lengthy delay then ensued as a new corner flag was found to replace the one Mbenza kicked over and snapped in celebration.
And the wait at least gave United time to awake from their slumber.
Rashford and teenager Tahith Chong, who replaced Sanchez, forced Lossl into saves low to his left.
Pogba then hit the crossbar for the second time in the game with a curling effort from the edge of the area.
But in their desperation for a winner, United could have succumbed to another stunning defeat as De Gea was called on to deny Grant a memorable winner.