Charlie Adam put the hosts in front in the 26th minute with a shot on the turn from close range.
Stoke continued to carve out opportunities, with captain Ryan Shawcross going closest by nodding against the bar, but were unable to add to their tally.
Pulis said: "I'm really disappointed we have not won the game by more goals.
"Even just looking at the first half, if you look at the chances, Robert has missed a point-blank header from a corner and Ryan hits the bar when he is almost under the goal.
"There were some great opportunities and in the second half we had more.
"Then in the last few minutes, you are starting to scramble.
"We had so many chances and you get a little bit uptight because you know one mistake could have cost us the game - a game that we should have been out of sight in."