Arsenal will be left needing an unlikely result from already relegated Norwich City in order to finish in the top four after they were deservedly beaten at Newcastle.
The Gunners went down 2-0 at St James' Park on Monday evening to hand the top four initiative to rivals Tottenham Hotspur on what was a hugely damaging night.
Ben White deflected a Callum Wilson effort into his own net for the Magpies' opener in the 56th minute, before Bruno Guimaraes followed up another Wilson effort to double the lead late on.
In truth Arsenal didn't deserve anything from the game, and the loss has left them two points behind Spurs - to whom they lost 3-0 at the Tottenham Hotspur Stadium last week - ahead of the final weekend of the season.
Spurs now sit in fourth with 68 points from their 37 games, while Arsenal have 66 from their 37.
Antonio Conte's side go to Carrow Road to take on Norwich on Sunday, while Arsenal are at home to Everton at the Emirates Stadium.
Given that Spurs have a vastly superior goal difference over their rivals (+24 compared to +9) that means in reality Conte's side now only need a draw against their already relegated hosts to earn qualification for the Champions League, something they will be expected to do.
Arsenal will have to beat Everton and hope that Norwich somehow cause a shock against Spurs.
Speaking after Sunday's 1-0 win over Burnley, Conte said: "It's not easy to play against Burnley.
"They tested our nerves because it was vital to get three points. We had to do our task and win to put some pressure on Arsenal.
"We know very well it is not easy to play against Newcastle, especially since the arrival of the new manager.
"They are in a good spell and it is not an easy game. I will watch the game because I love football and I want to watch and I want to suffer."