Pulis was booed by home fans during defeat to West Ham United.
Shawcross said: "The manager puts the team out there to win and I thought he put out a very attacking team on Saturday, but we didn't perform.
"It is definitely on the players' heads."
And Shawcross, who was first brought to Stoke by Pulis in August 2007, said the players remained united behind the manager.
He also told The Sentinel: "There's never been any doubt about that. He has been back at Stoke for seven years now and has done fantastically for the club; people soon forget how well he has done.
"He has done great for us and I am one of the players who thinks he is a top manager.
"He will get us out of this run and we will soon be on a winning run again."