Arsenal have historically struggled against sides with an aerial threat but Carroll was kept largely quiet throughout yesterday evening's game.
"You never can completely control Carroll for 90 minutes," Arsenal's official website quotes Wenger as saying. "You have to fight for him and be good on the second ball.
"The problem with West Ham is not only Carroll, but [also] Nolan on the second ball in the box. We could have been punished once or twice but overall we gave it all to deal well with him.
"Carroll was really up for it I must say. He did fight from the first to the last minute."
The win has put Arsenal in fifth place until the resolution of today's games.