The midfielder saw red in the 71st minute of an action-packed game for what referee Mark Clattenburg clearly thought was a dangerous, over-the-top tackle, and Cork reacted as if he had been badly hurt.
Pulis said: "I've spoken to Mark about it and he's going to have a look at it and then take a view from there. You've got to be careful what you say. It's disappointing but you have to get on with it.
"I was disappointed with the reaction of the player. That didn't help. I'm a great advocate for players getting up and getting on with things and that doesn't help referees.
"Whether the reaction of Cork, who is a good player and a good lad, has influenced Mark, I'm not sure, but Steven certainly doesn't stamp on the player. There was no intent. He's actually planted his leg between his legs, which was quite clever."
Rickie Lambert opened the scoring in the 10th minute but Kenwyne Jones made amends for an awful miss by equalising with a smart backheel six minutes later.
A mistake from Robert Huth, who miscued a clearance against the bar, presented Jay Rodriguez with Saints' second in the 24th minute, and 12 minutes later Andy Wilkinson's own goal made it 3-1.
Southampton should have extended their lead but Asmir Begovic saved Rodriguez's shot and Guly Do Prado missed an open goal from the follow-up, and they were made to pay as Stoke went down the other end and Upson scored from a corner in the 67th minute.
Nzonzi's sending-off came only four minutes later but Stoke kept pressing and got their reward in the 90th minute when substitute Cameron Jerome let fly with a stunning 30-yard volley that flew in off the underside of the bar.