Lukas Podolski's deflected free kick was enough to give the Gunners all three points, moving them one point behind fourth-placed Tottenham Hotspur.
Spurs have a game in hand over Arsenal, but Wenger believes that his side can build sufficient momentum to overhaul their North London rivals if they keep up their winning ways.
"I said already before the West Ham and Liverpool games, that we are in a position where we cannot drop points," said Wenger.
"We dropped two points against Liverpool but we couldn't do it again today. What is more important is the quality of performances is there. The spirit is there.
"The target to be in the top four and to focus on the two cups we are still in is very important now as we have strengthened our belief and our confidence."
Tottenham's game in hand comes away to West Bromwich Albion tomorrow.