Arsenal's 2-1 reverse at Old Trafford on Saturday ensured the club have made the worst start to a Premier League season since Wenger took charge as manager and left them nine points adrift of United.
Qualifying for the UEFA Champions League is now likely to be the main challenge for the Gunners and Wenger wants his team to prove their credentials.
"We're very far behind now," said Wenger. "At the moment you cannot say that [we are good enough to challenge the top three], because we are far away.
"But that's what we have to show, and that's what the target is at the end of the season. We've played away at United, City, Liverpool and Stoke - so we've many difficult away games.
"But we were poor defensively here. There's no obvious reason for that, apart from the fact we didn't start well and United have quality up front.
"They score goals against everybody and they are better than us. It's as simple as that.
"Away to Manchester City we drew 1-1, a good result, and didn't suffer by comparison.
"Here, I just think we were not on full cylinders and looked much more vulnerable defensively than we did at the start of the season."