Jack Collison came off the bench to score the winner deep into first-half injury time after being found by fellow substitute Ricardo Vaz Te.
Andy Carroll and Ryan Shawcross had gone down to the ground in the run-up to the goal and Pulis believes the Stoke defender had been fouled.
He told Sky Sports: "We're disappointed with their goal. Ryan goes to step in front of him and Carroll pulls his shirt and pulls him down.
"Like I say, we're really, really disappointed that the referee has not given a free-kick there."
Stoke were also denied two second-half penalty appeals when Cameron Jerome was challenged by Joey O'Brien in the box and the ball hit Guy Demel on the hand late on.
Pulis added: "The second one definitely hit his hand. But if we go to the game, forget the referee, I thought we huffed and puffed, I didn't think we got enough quality into the box.
"Playing with strikers today, they need a little bit more service than what we've given them and we just didn't get the crosses in to service them.
"People criticise the forwards not scoring goals but they've got to have good service.
He added: "We've gone a little bit flat without a question of a doubt but we'll keep going."