The England star later retracted the comments and apologised to both clubs for his attack.
"Actually I thought it was a compliment! I know Steven has apologised for what he's said but I actually took it as a compliment that Everton play like Stoke," he said.
"Everton have done fantastic this season and are a good side."
Pulis added: "I've got a great respect for Gerrard. He's a great advert for English football.
"Was I surprised? No. People know me by now and I don't give a flying...
"I don't take the criticism to heart, if it could even be classed as criticism."