Despite guiding the Hammers back into the Premier League at the first time of asking and making an impressive start to the current campaign, Allardyce remains an unpopular choice among some fans due to his perceived 'ugly' tactics.
However, Pulis, who has also been accused of employing unattractive tactics, believes that Allardyce's results speak for themselves.
"I don't think he pays too much attention to what people do or do not think. He gets the job done and he has done a wonderful job at West Ham. It was very difficult for him. They played in the Championship, were the top team in the Championship and everyone would have wanted to knock them off their pedestal," said Pulis.
"It is difficult when it is like that, but he got them promoted in one season and they have had a great start this year. He has been a very successful manager and maybe at times he doesn't get the praise he deserves.
"They must be absolutely doing somersaults at West Ham at the moment, and he deserves a hell of a lot of credit for that. I think the important thing as a football manager is that you play to your strengths and according to what you have got. You would have to ask Sam what he thinks of the criticism he gets, but the one thing I do know is that he gets results."
Stoke and West Ham face each other in the Premier League tomorrow night.