The Potters did get one, and Jonathan Walters converted it to put Pulis' side 1-0 midway through the second half at St James' Park.
But Pulis felt another spot-kick should have been awarded for Davide Santon's first-half challenge on Ryan Shotton - though the incident happened outside the area.
Perhaps with more justification, he suggested that matchwinner Papiss Cisse might have been sent off for an altercation with Marc Wilson and Ryan Shawcross.
"We are desperately disappointed," said Pulis following Stoke's 2-1 defeat.
"We could have had a penalty in the first half; the incident where Cisse was involved with Ryan and Willo - on another day, something could have happened with him and he might not even have been on the pitch.
"The referee deemed that it was alright. Fine, if he's still on the pitch, we should defend better.
"But I am disappointed, absolutely distraught with the result, but the performance and the effort and the commitment of the players was absolutely first-class."