Kuyt's treble was the first time he had scored against his fellow Dutchman.
Kuyt said: "You always dream about a hat-trick and to get one against United is the best feeling ever.
"Edwin (van der Sar) told me after the game that I don't score many against him, but today I got a hat-trick, so I'm more than happy with that.
"I have to thank Luis (Suarez) as well because I thought he had a fantastic game. He created two of the three goals. We have belief that we can compete against the best. We showed that against Chelsea and now we've shown it against United."