Arsenal manager Mikel Arteta said it was a "big disappointment" to exit the Europa League following a 2-1 defeat at home to Olympiakos.
The Gunners took a 1-0 lead into second leg at the Emirates but fell behind to an Abou Cisse header seven minutes into the second half.
It looked like Pierre-Emerick Aubameyang's stunning overhead kick in extra time would be enough to send Arsenal into the last 16 but Youssef El Arabi's goal in the 119th minute settled the tie in favour of the Greeks.
There was still time for Aubameyang to win it in injury time of extra time but the Arsenal captain somehow missed the target from five yards out.
Arteta said: "It hurts, big time. We had a lot of hope in this competition. It was a great way for us to be able to go to Europe and it is a very beautiful competition to try to win.
"I think we did a lot of positive things in the game. I think we created enough chances to win the game, but if you concede two set-pieces again in a tie like this, then you put yourself in big trouble."
"We’ve done the most difficult thing to react after that (going 1-0 down) and play against a team with 10 men behind the ball in 25 metres.
"Even at the end we had an incredible opportunity to win it."
"If we would have gone through, energy wise it would have given us a big lift again and bring everybody together.
"It’s a big disappointment and I’m right behind the boys, the way they played, the way they tried, the effort that they put in the game was enormous and we have to move forward together."