Jack Collison scored the only goal of the game just before half time but after the break, the Potters saw a claim for a penalty turned down when Guy Demel appeared to have handled the ball inside the area.
"Their goal is really hard to take - Carroll actually pulls Ryan down and we are disappointed with that and we could have had a penalty in the second half," Pulis told reporters.
"We thought it was a definite handball. But like the offside rules, handball is a very ambiguous topic at the moment. You are hoping that will give you a break but we didn't get a break."
Stoke are 11th in the Premier League following their defeat at the Britannia Stadium.