Since replacing Ian Holloway in November, Pulis has overseen a fine revival at Selhurst Park, turning around the fortunes of a side tipped for an immediate return to the Championship.
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Jerome, who also worked with Pulis at Stoke City, believes the experienced boss deserves all the praise coming his way.
"He is definitely up there," Jerome told reporters. "Jose Mourinho said last week, from where we were to where we are now speaks for itself.
"It's not necessarily the manager that wins the league who is the best; it's the one who has done the best job.
"I think with the resources he has got, the amount of people that have written him off, Tony has done an unbelievable job.
"He deserves every plaudit that he gets. He had a point to prove coming here and he's the sort of man who relishes that sort of challenge.
"If he manages to keep us in the Premier League, he will have done a fantastic job. His tactics are spot on.
"You can talk about other people being 'The Special One' and this or that, but he doesn't get enough credit for the way he plays.
"People say he's one-dimensional and plays long balls, but he's got Premier League experience. He knows what it takes to stay in this league."