The result brought United's 100% start to the Premier League season to an end and it was the first time the Potters had taken points off Sir Alex Ferguson's team since being promoted to the top-flight in 2008.
It also meant Stoke have now lost only one of their 12 games in all competitions so far this term, and manager Pulis wants to see no let up going into tomorrow night's Europa League Group E home clash with Besiktas and Premier League trip to Swansea on Sunday.
"It was a great performance and we really enjoyed it," Pulis said.
"The crowd were amazing - it was one of the great games of the football club, in respect of the atmosphere and the commitment of the players of both Stoke City and Manchester United.
"But that is gone now and we have two massive games coming up. I think the biggest risk to us is complacency."
United took on Stoke without Wayne Rooney, who was sidelined by a hamstring injury that also kept him out of their 3-3 Champions League draw with Basle last night.
Pulis admits the absence of the 25-year-old - scorer of nine goals for his club already this campaign - on Saturday was a major boost for the Potters.
"On the right day, United can be as good as Barcelona," Pulis said.
"But we've played them, and I have to say this - not seeing Rooney's name on the teamsheet was a massive bonus for us.
"I think this season Rooney has been different class and that he has been the difference at times.
"He is the glue that has kept everything together for them and it is no surprise that when he is not involved, like last night, they don't get the result that they are desperately keen to get.
"Wayne has been a massive miss for Alex in the last two games."
Source: Team Talk
Source: Team Talk