The result brought United's 100% start to the Barclays 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 Pulis wants to see no let up in Thursday night's Europa League Group E home clash with Besiktas.
"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."
Besiktas midfielder Ricardo Quaresma, who briefly played for Chelsea in 2009, knows all about Stoke's physical approach but has backed his side to pick up where the left off in Europe after hammering Maccabi Tel Aviv 5-1 on matchday one.
"We know that Stoke are a tough team, who play with the ball high. But we know ourselves too, and we know what to do," said the Portuguese.
"In 90 minutes anything can happen. It is not going to be easy for us, but the important thing for us is stay calm, play our football and then we will see what happens.
"We know that in English football a lot of fans come to the stadiums to support their teams. But we are used to this kind of atmosphere when we play, so it will not be a big deal for us."
Besiktas coach Carlos Carvalhal has warned his players to be on their guard against the threat of Stoke striker Peter Crouch, who hit the equaliser against United at the weekend.
"He is a difficult player," said Carvalhal. "We know him very well - we saw the match against Manchester United and he scored a good goal.
"He is the kind of player who is fantastic for the way Stoke play. But we are prepared for this kind of football."