Papiss Cisse struck two minutes into stoppage time to complete a comeback after Stoke had threatened to snatch victory at St James' Park.
Jonathan Walters had given the visitors the lead against the run of play from the penalty spot with 67 minutes gone, but Yohan Cabaye's superb free kick six minutes later set the stage for Cisse's last-gasp winner.
"Papiss Cisse could easily be off the pitch," Pulis said.
"He raised his hands twice; he pushed Andy Wilkinson and then he slapped Ryan Shawcross. He raised his hands and caught Ryan round the face."
The win takes the Magpies nine points clear of the relegation zone, but leaves Stoke without a win in nine matches.
"Away from home we've played better this season than at any time in our five years in the Premier League, we've been in more games, we just haven't been able to get over the line," Pulis said.
"It's really frustrating and disappointing because the lads have put such an effort in again today."
The win was just what the Newcastle manager Alan Pardew had asked for to end a good week and while it was deserved on the balance of play in front of a crowd of 50,703, it looked like evading his side until the very end.
Within minutes of the final whistle in Thursday night's 0-0 Europa League draw with Anzhi Makhachkala in Moscow, Pardew immediately turned his attention to Stoke and the business of securing three points.
With the goalkeeper Rob Elliot accepting the responsibility to deal with his share of the inevitably aerial assault, the Magpies were largely untroubled during the opening 45 minutes.
As the half wore on, Newcastle adopted a more intelligent approach with Cabaye prompting and Moussa Sissoko driving at the heart of the Stoke rearguard.
The deadlock was broken with 23 minutes remaining when, after Cheick Tiote had felled Walters inside the box, the referee Andre Marriner had little option but to point to the spot and Walters duly obliged to give the visitors a lead they scarcely deserved.
However, the lead lasted barely six minutes as the game became increasingly lively both on and off the pitch.
Sissoko was tripped by Glenn Whelan inches outside the box and after Marriner awarded a free kick, the goalkeeper Asmir Begovic became embroiled in a row with Steven Taylor as the Stoke coaching staff took exception to Pardew's reaction on the sideline.
But once order had been restored, Cabaye curled the free kick over the wall and in off the underside of the crossbar to level.
There was even better to come in injury time when the substitute Sylvain Marveaux picked out Cisse in front of goal and he controlled and fired past the stranded Begovic to snatch victory.
* Press Association
Follow us @SprtNationalUAE