Potters boss Pulis was fuming with the Blues stars, despite their failure to win penalties in the match and the fact Oscar was booked by referee Michael Oliver.
Ivanovic, though, escaped a caution after throwing himself down in the box in the first half when he appeared not to be touched.
Pulis also insisted Chelsea should have ended their 1-0 victory with 10 men after David Luiz was shown a yellow - and not a red - card for a crude lunge on Jonathan Walters.
Highlighting what he dubbed "the simulation", Pulis said: "Ivanovic's one in the first half is laughable and the lad Oscar, who's a fabulous player.
"This is England. We're playing in England, we're not playing in Europe.
"And we can't watch people just fall over and not talk about it. That's the disappointing thing.
"We should highlight it and keep highlighting it and keep highlighting it.
"There are certain players in the Premier League who have got a reputation and referees know that if you touch them then they'll fall down or go down as quickly as they can.
"The people that do it, just keep highlighting it, keep showing it, because it's a part of the game that I don't think we should stomach and we don't talk about enough."
He added: "I think there were four occasions today [Saturday]. The referee did smashing.
"But that's the other point. They put enormous pressure on by falling over.
"It's difficult enough today to referee anyway.
"And for players to be doing that, I don't think it's fair on the referees."
Pulis said of the Luiz lunge: "It's a dreadful challenge and I think David would be the first one to say he's very, very lucky to stay on the pitch - very."
Asked if it would have been a red card had Luiz been a Stoke player, Pulis said: "Now you said that, not me. Make sure the FA know it was you."
Pulis also claimed Stoke striker Peter Crouch felt he should have had a first-half penalty himself.