A stuttering first-half performance frustrated the supporters at the Emirates Stadium but with the score at 1-1, the hosts struck four times in the space of 10 minutes to secure the three points.
"It was a tough first half for us," the midfielder told Sky Sports News. "We knew what West Ham bring, they're a physical team and they get behind the ball and defend.
"They got a good goal so we had to come out and play and in the second half for 15 minutes we really upped our game.
"It was a good game for us and we're happy with the three points."
Arsenal are now sixth in the Premier League.