Stoke defender Abdoulaye Faye was sent off in the 53rd minute.
Glenn Whelan sent Stoke in the lead while Gareth Barry grabbed an 85th-minute equaliser.
Stoke defender Ryan Shawcross had a goal disallowed at the death for a foul on given.
“Ryan’s goal was a good goal,” Pulis told Sky Sports. “But it’s been pulled away from us by a poor decision.
“He’s up in the air and Given’s done exactly what Aston Villa’s Stephen Warnock did against us a few weeks ago.
“He made contact with the player and falls down as if he’s been pushed. You have a look at Kolo Toure’s reaction when Ryan scores – he’s absolutely devastated because he things they’ve lost the game.
“But the referee doesn’t give it and we get too many decisions like that against us.”
The Stoke boss added: “When it was 11 against 11, we were the better team.
“We played with good passion and good commitment, and when a player gets sent off it’s difficult for us.”