Wilshere stressed that they cannot afford to drop points now as they push for UEFA Champions League football.
He told Sky Sports: "It was a tough first half for us. 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.
"We know the football we can play and that was that.
"It was a good game for us and we're happy with the three points."