Manager Arsene Wenger admitted he was devastated after his last chance to lift silverware with Arsenal went up in smoke.
The Gunners were beaten 2-1 on aggregate by Atletico Madrid in the Europa League semi-final after last night's 1-0 loss in Spain.
Former Chelsea striker Diego Costa returned to the Atletico side to haunt Wenger's men again and it was his composed chip on the brink of half-time which ended Arsenal's hopes.
"It is very, very sad but unfortunately you have to go through this in our game. It can be very cruel but sometimes it is nice. The suffering is tough tonight," said Wenger, who will leave the Gunners at the end of the season after 22 years in charge after failing to win a European trophy with the club.
"Atletico played with fear in the first half that if we scored they could be out, but once they scored they played with a cushion. We lost possession and Diego Costa is one of the best strikers in the world."
Arsenal captain Laurent Koscielny was carried off after tearing his Achilles early in the first half and will miss the World Cup.
Two-time champions Atletico will now face Marseille in their third Europa League final in eight years in Lyon on May 16.
Arsenal were crestfallen going into the break but almost responded within minutes of the restart when Aaron Ramsey found himself through on goal. His touch let him down and the chance was wasted - as were a number of opportunities for the visitors throughout the second half.
Defeat for Arsenal means they will miss out on Champions League football for the second straight season.
Wenger has three matches left before he officially departs.
After hosting Burnley on Sunday in his last home match in charge, Wenger takes his side to Leicester next Wednesday before saying goodbye after 22 years with an away game at Huddersfield.
The Gunners chief added: "It was a similar game to what we had in the first leg.
"The dangerous situations we created were there but we missed something in both boxes.
"We played a good team and good luck to them in the final but we feel we did enough to go through.
"We didn't manage the important moments of either game well.
"We were 1-0 up with 10 minutes to go at home, and then we conceded a stupid goal.
"Tonight we looked okay and then conceded on the counter attack."
On Koscielny's injury, Wenger said: "It is an Achilles rupture and maybe we will have good news, but the first signs are not very good."
Former Gunners defender Martin Keown was highly critical of Mesut Ozil's display in the Spanish capital, saying the German World Cup winner was not fit to wear the Arsenal shirt.
"I bet he doesn't play again this season," Keown said.
"He will have some emotional breakdown and won't be able to play at the weekend.
"I don't know how many illnesses he has had this season but the fella is not kidding me.
"That is not a proper performance.
"He isn't giving everything and there is a lot more under the bonnet.
"He wasn't fit to wear the shirt for me tonight and I have seen this a lot this season and it needs to be said.
"He needs to be dug out because we expect better from him. He is a World Cup winner and these are crocodile tears I am seeing from him and he is not conning me.
"I have had my say on it and I don't feel he is giving enough for Arsenal Football Club.
"Maybe Arsene Wenger should come out and say more about some of these players that should have performed for him and he is one who hasn't," fumed the former England defender after the game.