The Dutchman scored the first and last goal in the 3-0 win against their north London rivals at the Emirates.
He told Sky Sports: “They played with the right attitude, good spirit.
“It was a tight, tough first half hour, but from the moment we scored the first goal they died basically.”
Van Persie also hailed team-mate Cesc Fabregas’ wonder striker in the game.
“(It was) his brilliance,” said the Holland striker.
“Straight from the kick-off (Wilson) Palacios lost the ball, he went past Palacios and through Ledley King. To do that you need a lot of technique.”
