The midfielder was shown a straight red card in the 71st minute by referee Mark Clattenburg for a challenge on Jack Cork.
Pulis said: "The disappointing thing is Steven's sending off. Steven has moved his foot across, Cork's on the ground and he has planted his foot in between Cork's legs. I don't think there is any intent there at all for him to hurt the lad.
"I think what might have affected the referee was Cork's reaction. Steven hasn't stamped on him and hasn't touched him with the leg that goes on the ground.
"So that's a disappointment for us and we will certainly be appealing. I am just hoping that Mark will have a look at it and, after some of the incidents that we have been involved with this year, that he will look at it favourably for us as a football club."
Stoke trailed 3-1 after 36 minutes before mounting a second-half fightback with Cameron Jerome's stunning late goal securing a point.
Pulis added: "I thought we were awful first half and really that was as poor as we have been at both ends of the pitch.
"Kenwyne Jones' chance where he misses it early on, it is harder to miss than score and that epitomised everything we did. We were poor defensively, we gave poor goals away and we just looked off the pace. They were still tapping themselves on the back from the Liverpool performance.
"But second half we played with a lot of spirit and a lot of commitment and in the end even with 10 men we are disappointed we have not won the game."