It was a third straight Premier League defeat for Stoke, who have now won just one of their last 21 away league games.
Pulis's side were blown away by three second-half goals, including a double for midfielder Jonathan De Guzman, and had just a late Michael Owen consolation to show for their efforts.
"We were second best from the first whistle to the last," Pulis said.
"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 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."