West Ham, for whom James Collins had sent a header on to the bar prior to Jack Collison's goal, twice survived scares in stoppage time at the end of the match to hold on for the victory.
First, Stoke substitute Charlie Adam cracked a volley against the bar and the hosts then had appeals that Hammers defender Guy Demel had handled in the area waved away by referee Jonathan Moss.
Pulis felt the incident involving Demel should have resulted in a spot-kick, although he seemed more aggrieved about one in the build-up to the goal that featured West Ham striker Andy Carroll and Potters skipper Ryan Shawcross.
Ricardo Vaz Te was able to slip in his pass to Collison after attempting to play a one-two with Carroll and having the ball come back to him via a coming-together between the England forward and Shawcross.
Regarding that, Pulis - whose side's defeat was only their second at home in the top-flight this term - said: "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.
"We thought it was a definite handball. But like the offside rules, handball is a very ambiguous topic at the moment.
"They can say it is handball for one thing and not for something else in a similar situation.
"You are hoping that will give you a break but we didn't get a break."