The Gunners came from a goal down to secure the win, which moves them back up to fourth in the Premier League table.
The manager told BBC Sport: "I think we built the victory tonight through consistency in our game, the vital thing tonight was to come back to 1-1 before half time. It was a hard-fought win and a very enjoyable win as we had to dig deep on Saturday.
"We were under absolute pressure to win the game, on top of that it was a derby and after giving a lot on Saturday it was difficult. Maybe we could have scored more, I was satisfied with the mental response of the team tonight, the focus tonight of the team was outstanding.
"We showed maturity not to panic when we went 1-0 down, I had to rest a number of players tonight but it was good that players like Kim Kallstrom managed to contribute tonight."
Arsenal have a rehearsal of the FA Cup final when they face Hull City this weekend.