Arsene Wenger told his Arsenal side to be proud of their
Having capitulated 4-0 at the San Siro in the first leg, the Gunners were given next to no chance of making the last eight but stunned their visitors with an irresistible first half display that yielded unanswered goals from Laurent Koscielny, Tomas Rosicky and Robin van Persie with a penalty.
The energy exerted in that 45-minute burst told in a slower-paced second period, but Van Persie did miss with one superb chance to make it four from close range.
''They can only be proud of their performance,'' Wenger told Sky Sports 2. ''The team has fantastic spirit and showed some fight after the first tie, but unfortunately we go out. We had the chances for a goal, but we keep our winning run going which is important.
''We have paid the price for a bad first game. But we have given everything. That is all you can do at the top level: give everything and then you can accept the result.''
Arsenal were missing injured pair Aaron Ramsey and Mikel Arteta in midfield and, having used the impressive Alex Oxlade-Chamberlain centrally for the first time, Wenger felt more depth in the middle could have seen his side over the line.
''We were a bit short in midfield and on the bench we suffered a little bit. We got tired in the second half, we needed to keep the ball better,'' he said. ''We were the more fatigued and I'm sure we would have scored two or three more goals in the second half (with a fully fit squad).''
Van Persie has been inspirational for the Gunners this season and Wenger could not have wished for the final chance to fall to anyone else. But the Dutchman was not able to get a clean shot away and Christian Abbiati was able to make the save.
Asked about the chance, Wenger said: "I felt he wanted to chip the keeper, because he was down but Abbiati got up very quickly. He reacted well and unfortunately we couldn't score. I hoped in the last 10-15 minutes we could create some danger in front of goal but it didn't happen.''
Milan coach Massimiliano Allegri cut a relieved figure as his side avoided what would have been one of the greatest comebacks in Champions League history.
Of Milan's wretched first half performance he said: "We played with three forwards and certainly suffered too much.
"We conceded on the first corner and that made a big difference psychologically, then we made too many mistakes in our midfield passes. I'd say we got the game completely wrong from a technical point of view, as we were sitting too deep and played between defenders, but after the break we did move more in attack.
"It's a shame about the defeat, but the objective was to get through to the next round. Now we have time to get a few more players back from injury and continue in this competition. I did not see the team afraid as such, as there are experienced players here. In the locker room I simply told them we had to wipe out the first half from our memories and start from 0-0.
"In any case, I am not too worried. It was a crucial game and would've been a truly massive psychological blow for the rest of the season if we'd gone out from 4-0 in the first leg."
Defender Philippe Mexes said: "The first half went badly and they punished us on every single incident. After the break we were finally able to pass the ball around and we were consequently less afraid.
"This must never happen again. After a game like this, we have nothing to celebrate. We want to progress in the competition, but must do better, even if we got through to the next round tonight."