Stoke beat Liverpool two weeks ago.
But Shawcross told stokecityfc.com: "It's definitely the best result since we got in the Premier League in my opinion, especially when you consider the form that they have been in this season.
"Anything against the Champions is fantastic, and people may say we could have won it, but they had their chances too, especially Giggsy right at the end.
"I enjoyed that game as much as I have enjoyed any in my career. It was fast, it was action-packed and it was exciting. We had chances, they had chances, it had everything really.
"A point against United is fantastic for us, and to come off the back of the games we have had at the Britannia Stadium and remain unbeaten is a superb achievement."