A hat-trick by the Dutchman helped Arsenal grab a 5-3 victory at Stamford Bridge.
“You could see how happy we are at the end because we fought hard and every one of us showed character,” Van Persie said on Sky Sports.
“It’s a big, big win for us today.”
When asked about his second goal for the Gunners, Van Persie added: “I was surprised (when Terry slipped) because it was an easy back pass and I only saw later that he slipped because I was closing him down.
“I suddenly realised I was one on one with (Petr) Cech and a couple of things came to my mind to do, but I did the easiest one.”