The Potters were reduced to 10 men in the closing stages when Ryan Shotton was handed a second yellow card but replays showed he made no contact with Villa substitute Fabian Delph.
Pulis was also unhappy after a first-half challenge by Villa defender Ciaran Clark on Stoke midfielder Glenn Whelan went unpunished.
He said: "As regards the Shotton red card, I've just looked at the incident and we are very disappointed.
"I was also disappointed with the challenge in the first half (by Clark) and the way that was dealt with.
"When you see a lad getting sent off for two bookables which you can't appeal against, it is very hard to take.
"You look at the incidents and decide what you think. I don't want to get in trouble again. It has cost me enough money over my career!
"You can't appeal two yellow cards which I find amazing."