A win would have taken the Gunners to within a point of second placed Chelsea but as it stands, City have a game in hand at home against Stoke, with a win seeing them leapfrog Arsenal in the table.
With the top three in the Premier League assured of automatic Champions League qualification, the fourth placed side face the potential banana-skin of a two-legged qualification tie - which almost provided a stumbling block for Tottenham earlier this season.
After the game, Wenger admitted that failure to finish in the top three represented a poor return for his side who were fighting on four fronts just a few weeks back, yet have now slumped to three defeats in their last four Premier League games.
"Of course we are frustrated," he told reporters.
"We dropped three points today that could cost us automatic qualification for the Champions League. It will be a big setback to finish fourth.
"We have been hit hard recently by bad performance and results. You can see we suffered at the start today but we have to raise above that. We were nervous defensively."
Wenger's tormentor was Darren Bent, who clinically struck twice inside the opening twenty minutes to provide an insurmountable challenge to the Gunners.
Despite the impressive nature of Bent's finishing, Arsenal looked rocky at the back, with their central defensive pairing easily breached.
Thomas Vermaelen was returning after nine months on the sidelines as Sebastien Squillaci looked woefully short of confidence before being pulled off at half-time.
"We were punished because we went into the game too tentative and we gave cheap goals away," said Wenger.
"They [Vermaelen and Squillaci] are two players of experience and normally they should be able to work together, but I don’t know.
"Vermaelen looked stronger and stronger as the game went on, and of course he hasn’t played since September. Soon he will be dominant like he was before."
The result lends gravity to the recent clamour for a massive upheaval at the Emirates over the summer, a feeling that was made tangible by boos throughout the game and a mass exodus before the obligatory lap-of-honour at the end of the game.
The ground quickly emptied at the final whistle, giving the lap less a feeling of celebration than apology.
"It was not embarrassing," said Wenger of the proceedings after the final whistle.
"It’s our job to thank the fans and you never have to be embarrassed when you do your job.
"It wasn’t a lap of glory, of course, but no matter the result, you have to respect your fans for turning up. It is not an ego trip – it is a respect trip.
"The fans want to win football games, when we don’t they are not happy.
"We will try to strengthen of course, but the best way to keep our fans happy is to win games."