Moyes felt on another night, United could have left north London with all three points.
He said: "I thought we did a lot of good things in the game. We had good shape and were nice and compact. We had some good moments in the game.
"We had a great chance in the opening minute. I thought whoever would have got the first goal it would have been important and we had a great opportunity to get that.
"It (Van Persie's chance) was a great move, A great ball from Wayne Rooney and a great header. The goalie made a great save and near enough pulls it out of the back of the net.
"On another night Robin might have had a hat trick. He had three good chances."