The Gunners are in sixth position, seven points adrift of the Champions League places.
The under-fire Arsenal manager, who has yet to reveal whether he will sign a new contract with the Gunners when his current deal expires at the end of the season, declared himself satisfied with the character shown by his side in twice recovering after falling a goal behind to City.
But a solitary point left the Gunners in sixth position, seven points adrift of the Champions League places although they do have a game in hand on City who lie fourth.
Arsenal have qualified for the Champions League in every full season that Wenger has been manager of the north London club since the Frenchman's arrival in 1996.
But that proud record is under threat, with Gunners striker Danny Welbeck telling Arsenal.com: “At this point in the season and in the position we’re in, we know it’s not good enough for us as a club.
"We want to be further up the league. It wouldn’t have been good for us to lose three points again (against City), so we’ve dropped two. It’s something we’re going to have to build on in the next game.”
The England international added: “We obviously want to build on our performances. The position in the league that we’re in at the moment is not good enough. It’s something we really want to improve on, so that’s what’s on our minds for the next game."
And Arsenal midfielder Alex Iwobi said: “We still believe that we can be in the top four, and that we can be in the title race as much as we can, but we’ll take it step by step and see where we end up at the end of the season.
"We just came back from the international break and our confidence is slowly coming back. We were able to get a good result against one of the best teams in the Premier League, so the confidence will slowly come back and we have to continue that on Wednesday."
Arsenal's Laurent Koscielny is a doubt for Wednesday's London derby after being forced out of the City game at half-time.
West Ham’s Slaven Bilic is another manager feeling the pressure after a run of six games without a win, the last four of which have ended in defeat including Saturday’s loss at relegation-threatened Hull City.
The Hammers' board responded to the Hull defeat by issuing a statement in support of their manager.
It read: "To end speculation once and for all, the West Ham United Board feel it necessary to announce that we have 100 percent faith in Slaven Bilic's ability to lead West Ham United."
But like Wenger, Bilic desperately needs improved results, with his side having dropped to 14th place, six points above the bottom three.
West Ham will be boosted by the return of Michail Antonio and possibly Mark Noble for the trip to Arsenal.
"Michail Antonio is looking really good,” Bilic told whufc.com. “He was 50/50 for Saturday, which gives him a good chance to make it for Arsenal.
"Pedro Obiang and Winston Reid are out, Diafra Sakho is getting back and Noble could play."