The Swans emerged comfortable winners thanks to a fine second-half performance following a turgid first half at the Liberty Stadium.
Teenage left-back Ben Davies got his first senior goal for the club before Jonathan de Guzman struck twice with a wonderful free-kick and a composed finish late on.
Michael Owen pulled a late goal back for the Potters, the striker's first goal since October 2011, but it was a mere consolation.
"We were second best from the first whistle to the last," said Pulis. "Swansea were better and deserved to win. I've got no excuses.
"You have good and bad days in football and this was a bad day for us. We looked a yard short all over the pitch. We looked sluggish and sloppy.
"Whether it's the fact we played (Crystal) Palace in extra-time (in their FA Cup third-round replay in midweek) and had to travel down early and had not been able to do anything for two days because of the snow, I don't know, but it wasn't us today."
But Pulis made it clear he does not need to sell players, including Swansea target Kenwyne Jones, who came on as a substitute, before he can strengthen his squad.
He said: "It's great speculation. If the two clubs are talking then they have to talk and speak to me and then I'll speak to Kenwyne.
"You always want to keep your top strikers. I'll be as open and honest as anybody. If an offer comes in for any player in the Premier League and it's the right offer then you look at it and then speak to the player."