The Latics went ahead inside five minutes when Robin Huth was adjudged to have handled Shaun Maloney's shot on goal.
However, the Potters twice came back from a goal down to earn a 2-2 draw.
Pulis declared himself pleased with the way his side bounced back from the early setback.
"I thought it was a soft penalty - Martin [Atkinson] is saying that [Huth] has stuck his hand out, but he's actually tried to take his hand away from the ball as quick as he can," said Pulis. "It was so close - you would have to be superman to move it away from that close.
"That was disappointing, but we bounced back, and then in the second half, the goal after a few minutes was a poor one to concede. But our attitude and character was fabulous.
"I thought we had the better clear-cut chances and the save from the goalkeeper was a fantastic save, unbelievable."
Stoke host Manchester City at the Britannia Stadium in their next Premier League fixture.