The Gunners were undone by Darren Bent's scrambled goal from a corner.
Defeat left the Gunners eight points adrift of Barclays Premier League leaders Chelsea, and manager Wenger admitted they had only themselves to blame.
He said: "We lost a game and we can only fault ourselves because we didn't score.
"Some players were not at their best and we gave a goal away on the only situation where Sunderland could score one today, a set-piece, and that sums it up well.
"Rather than focusing on any individual, I believe it's more down to the fact that we made a big mistake on the corner, because the game was there for the taking in the last 20 minutes.
"But of course, 1-0 down makes it more difficult."