Carlos Vela, William Gallas and Van Persie all had second half chances to improve the Gunners chances of a Champions League spot, but failed to find the target.
"We said we would try and keep a clean sheet and try and steal a goal. We had a little half-chance late on.
"We rode our luck a bit but we doggedly stayed in there. The defence and the midfield were excellent today. Overall I am really pleased.
"The longer the game went on we thought we probably had a chance, but to be fair they missed a couple of good goalscoring opportunities. We had a little bit of luck on our side."