Wenger praised the attitude of his players and described the result as "absolutely vital" as the season draws to a close.
"We will know at the end of the season how important this win is, but we knew as well the win was absolutely vital for us and we could not drop points," Wenger told reporters. "We have shown we are up for the fight and we will do so until the end of the season.
"The attitude of the players was outstanding, even when our legs were less than fresh after playing in midweek. We kept going and refused to drop points. The players knew what was expected.
"What we have done in the last three days is very difficult to do. To win away in the Champions League and then win away in the Premier League is very difficult and I would like to congratulate the players for that."
Arsenal now sit just four points behind third-placed Tottenham Hotspur in the Premier League table.