Arsene Wenger is sure “the players can be proud of that performance” after Arsenal “restored some pride” by beating Milan.
“I told the players they can only be proud of that performance,” said the manager on Sky Sports.
The Gunners almost overturned a 4-0 first leg defeat, but their 3-0 win at the Emirates  was ultimately not enough.
“We were a bit short with no midfielders at all on the bench, we suffered a little bit when we got tired in the second half, as I hoped to keep the ball better and get them more fatigued.
“I’m sure we’d have scored another two or three goals in the second half, but the performance showed fantastic spirit and we restored some pride after the first leg. Unfortunately we go out. We had the chances, we keep our winning run going and unfortunately we pay the price for a bad first game.”
When Arsenal were 3-0 up at the break, Wenger was asked whether he thought the work was done.
“No, not at all, we knew we had given a lot and had players not used to that level in midfield, like (Alex Oxlade-)Chamberlain. Some players had knocks, I knew it would be difficult.
“You need to score goals and not concede against a team like that. Our defenders were absolutely outstanding today and we have given everything, that is all you can do. If you’ve given everything then you can accept the result, even if it is a disappointing one.
“Chamberlain was sick last night, so we were not sure if he could play, as he had flu. We checked him in the warm-up, but he was outstanding. Of course to last at that level for 90 minutes is a different game.”
Robin van Persie had the best chance of the second half, but Christian Abbiati performed a miraculous save from point-blank range.
“I felt he wanted to chip the keeper because he was down, but Abbiati got up very quickly and unfortunately we couldn’t score.
“I hoped in the last 15 minutes we could create some dangerous situations in front of goal, unfortunately it didn’t happen, as we didn’t have enough drive anymore.”