Arsenal finished the season with a 5-1 thrashing of Everton but had to settle for a fifth-placed finish as Tottenham beat Norwich at Carrow Road
Arsenal needed the relegated Canaries to beat Spurs in order to have any chance of claiming the fourth Champions League spot but their emphatic defeat ensured it never looked likely on the final day
Arsenal enjoyed themselves nonetheless, moving into a commanding lead at the Emirates Stadium when Gabriel Martinelli scored from the penalty spot (27) and Eddie Nketiah struck from close range (31)
Everton substitute Donny van de Beek pulled a goal back with a tap-in on the stroke of half-time but Arsenal made their dominance count in the second half with goals from Cedric Soares (56), Gabriel Magalhaes (59) and the excellent Martin Odegaard (82)
The four-goal margin of victory made it Arsenal's biggest win of the Premier League season and took them to 69 points, two behind Tottenham, while Everton finish on 39 points in 16th having secured their Premier League survival with a game to spare
Arsenal never got any kind of grip on the game during Monday's costly defeat to Newcastle but they dominated right from the start on their return to the Emirates, pinning Everton back and creating a series of early chances
The first fell to Odegaard following a Nuno Tavares cut-back, but his low effort was repelled at close-range
 Asmir Begovic, standing in for the absent Jordan Pickford in goal, then had to be alert again to save a similar effort from Martinelli
Everton had a rare sight of goal when Demarai Gray's powerful drive forced a slightly panicked save from an out-of-position Aaron Ramsdale, but Arsenal's breakthrough arrived not long afterwards
They had to wait for a VAR check after Martinelli's initial shot had been blocked by former Arsenal man Alex Iwobi, but Andre Marriner pointed to the spot after consulting the pitchside monitor for handball and Martinelli made no mistake, sending Begovic the wrong way
The second goal arrived from another set piece as Bukayo Saka's corner was flicked on at the near post by Granit Xhaka and Nketiah, on what could prove his final Arsenal appearance, flicked the ball over the line from inside the six-yard box
Arsenal continued to pile forward, with Martinelli threatening a third following a goalmouth scramble and Saka firing narrowly wide after being put through on goal by Nketiah
But Everton suddenly found a way back into the game when Arsenal's defence switched off and Van de Beek, a substitute for the injured Abdoulaye Doucoure, tapped in from Dominic Calvert-Lewin's low cross after ghosting into the box unmarked
Everton briefly gained some momentum, making an improved start to the second half, but Arsenal soon reasserted their dominance, restoring their two-goal cushion through an unlikely scorer in Cedric as he slammed home from another Saka corner
The full-back was involved in Arsenal's fourth, too, as his attempted shot fell to Gabriel, who bundled the ball past Begovic, the goal surviving a VAR check for offside
Arsenal - and the home supporters in the stands - were well aware the win would not be enough for fourth given events at Carrow Road, but they continued to get behind the team and Odegaard's fifth was arguably the pick of the bunch
Having collected a pass from substitute Nicolas Pepe on the edge of the box, he shimmied away from Everton youngster Isaac Price before rolling a sublime, side-footed finish into the bottom corner
The five-goal performance was not enough to secure Champions League football, but it ensured a positive atmosphere and a happy send-off for the players as the club gear up for a big summer
 boss  said: "We did what we had to do
 We knew that it wasn't in our hands
 We needed a miracle and it didn't occur
 That's it
 The league table at the end of the season doesn't lie
"It's true that last year with 67 points, Chelsea got into the Champions League
 We have 69 we are out of it
 But that's the level and the demands this league has now
"We tried to give the fans everything they deserve, everything they have done for us and helped us to come much further as a club and as a team
"I cannot assess the season today, I'm sorry, I'm still in a lot of pain after what happened on Monday and I would like to have a fair assessment on what we've done
"What I can guarantee you is that we have tried to squeeze the lemon as much as we possibly could, for every single drop, and we reached the point that we reached
"You can see what we have on the pitch and what this club had on the pitch 10 or 20 years ago
 We know where we have to go and we are not going to stop
"We are disappointed today because we have generated expectations that we wanted for this football club and in the end we came short
 That feeling of guilt, and not reaching that level is painful
"Arteta: Nketiah, Lacazette, Elneny futures have been decided boss  insists decisions have already been made over the futures of,  and and says he will speak to the out-of-contract trio in the next two days
"I will speak to the three players now or tomorrow and after that we need to start to move on, but we have clear ideas of what we want to do," he said after Arsenal beat Everton 5-1 but still fell short of Champions League qualification on the final day
"It's been decided, but it's very difficult to communicate it while they deserve to have a little bit of what they had today
"To do it earlier, one way or the other, with three situations like that is very awkward and could affect the team
"As a club, we have to do the right thing in the right moment
 Sometimes to combine those two is not easy at all but we will try to do the right thing
" boss  said: "We spent a lot of energy on Thursday
 Richarlison, Allan and Andre Gomes were injured, while a few of the lads deserved a rest
"Our big final was on Thursday and we won it
 Today was just a step too far
"It's a difficult game for the players and Arsenal were playing for something
 I thought Tom Davies played well and Dominic Calvert-Lewin really showed his power
"My immediate feeling is absolute delight and relief that we kept the club in the Premier League
"When I came in, confidence was low and we had to deal with a lot of injuries
"The good thing about pre-season now is that we can work on things that we want to work on and improve the squad
"
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