Gunners stumble to semi-final.
An Antolin Alcaraz own goal set the Gunners on their way before Nicklas Bendtner added a second late on, taking Wenger's side through to the semi-final, but the Frenchman admitted he would rather get his hands on the Champions League or domestic championship.
"The supporters always want more [and that's] completely natural, but we have played for 14 consecutive years in the Champions League and many people would be happy with that," he told reporters after the game.
"We are not completely happy with that, the supporters want more and I can accept that.
"We want to make our supporters happy as much as we can. The major trophies and the Champions League and the championship but if we can win this competition we will take it
"You want to win trophies and always be at the top and you can only do as well as you can, at the moment we are in all competitions.
"You cannot say [the League Cup] is not important, but you have to not make an obsession of it. We want to focus on the quality of our performances, and the rest will be the consequences of our performances."
The game saw the first start for Robin van Persie since the Dutchman's ankle injury and after lasting 70 minutes, Wenger was pleased with his showing and that of his makeshift team.
"He showed class but still needs games," Wenger added. "It was difficult [for him] to play 70 minutes tonight, lets hope he can have no reaction from playing tonight and he will become stronger and stronger.
"We did the job [tonight], they closed us down well at the start of the game, but slowly as you gain control of the game we created chances and overall it was a good win.
"We made eight changes tonight, we still have no Diaby, Vermaelen, Alumnia, Squillaci, apart from the players we rested. I don't know where to put the players. I have to give them a chance, and we have already fantastic international players who do not get enough games."
The night's other quarter final saw West Ham shock Manchester United at Upton park with a 4-0 drubbing, and Wenger admitted he was as surprised as anyone.
He continued: "I look at the team Man United played and I don't really know what happened but they looked to have a strong team out.
"In the Premier League we have to accept that there is no guarantee that you will win the trophy, you have to fight, in every single game to win, and now [the semi-final] is home and away so it will be tough comp for us."
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