Thomas Vermaelen netted a consolation late one, but the Gunners are now four points adrift on United and five from leaders Chelsea.
And Wenger said: "It's difficult to accept but easy to explain because we were poor offensively and defensively. We delivered an off-the mark performance and that is why we were well beaten. We were naive."
Wenger admitted it was a major jolt to their title ambitions, adding: "It was not just Rooney who gave us problems. We gave them too much room everywhere. Rooney took advantage of it. "We conceded two goals from a corner for us and it turned into a goal for them. It was our positioning that was wrong.
"It is a massive blow and a massive disappointment but we have to recover from that. It is part of top Premier football. The players are really down."
Source: PA