Here is the reaction of the two managers.
Roberto Martinez
We worked really hard to restrict Arsenal but too many things affected us again. The injury to Victor Moses, the own goal... it was too much. Up until their first goal I thought we defended quite well.
And you really need to stop Arsenal scoring the first goal because your task becomes that much harder. Our main concern now is Victor, and Mauro Boselli also came out of the game with an injury, and the squad is looking quite thin at the moment.
We have done some good things in this competition, but now is time to concentrate on the league. We created a couple of half-opportunities that we could have maybe done a little better with.
I was pleased to see Callum come on at the end and he showed a really fighting spirit. Victor fell very awkwardly and straightaway you could see that he had dislocated his shoulder.
We sent him straight to hospital, and we'll continue to assess him. Unfortunately we are looking at anything between four to six weeks, and that's a shame because he looked very sharp tonight.
He got into a few one-on-one situations and he looked a real threat. We know how much we're going to miss Victor for the next few weeks. Injuries and suspensions are a reality of the game, and we have to adapt to it as well as we can.
A couple of injuries and a couple of suspensions mean it has been a tough month for us, but we have to concentrate on the next six or seven league games now before the FA Cup begins.
The ball hit Antolin and no-one knew much about it. We were very unlucky but we won't feel sorry for ourselves because we've had a good run in this competition.
The second goal was a real killer for us, and we couldn't manage to get any rhythm going after that in the final third. But we have to congratulate Arsenal for that and we wish them the best for the rest of the competition.
It's been a fantastic experience for some of the boys, players like James McArthur and Ben Watson, who haven't been playing too much football this season.
Arsene Wenger
You cannot say that [a first trophy] is not important, but we should also not make obsession of that. We want to focus on the quality of our performances, and the rest will be the consequences of those performances.
The major trophies are the Champions League and the [domestic] championship, but if we can win this as well, we will take it.
We want to win trophies and be at the top, but you can only do as well as you can. At the moment, we are at the end of November and are in quite a good position in all of the competitions.
Next up for the Latics is the visit of Stoke City on Saturday. Given the present position in the league, this is a big game for the Latics, and one that Roberto Martinez will be hoping for maximum points from.
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"The injury to Victor Moses, the own goal... it was too much. Up until their first goal I thought we defended quite well.
"And you really need to stop Arsenal scoring the first goal because your task becomes that much harder.
"Our main concern now is Victor, and Mauro Boselli also came out of the game with an injury, and the squad is looking quite thin at the moment.
"We have done some good things in this competition, but now is time to concentrate on the league.
"We created a couple of half-opportunities that we could have maybe done a little better with."