Allardyce has been criticised throughout his managerial career for employing what are perceived to be unattractive, long-ball tactics, but Pulis insists he deserves more credit.
The Hammers have made an impressive start to the new season after winning promotion under Allardyce last term, and Pulis is expecting them to give Stoke City a tough game.
Asked about Allardyce's detractors, Pulis - who has faced accusations himself of using a negative playing style to get results - said: "Each to their own.
"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.
"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."
Allardyce also got Bolton promoted from the second tier in 2001 and he subsequently guided the Trotters to consistent top-10 top-flight finishes, a League Cup final and into Europe, before departing in 2007.
After a brief spell with Newcastle, he then took charge at Blackburn, who he steered away from the relegation zone in his first season and then up to 10th in his second before being sacked by Rovers owners Venky's.
"He has been a very successful manager and maybe at times he doesn't get the praise he deserves," Pulis said.
"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.
"Look at when he was at Bolton and look at Bolton now (they were relegated to the Championship last season).
"They were finishing in the top 10 in the Premier League year after year. The fella knows what he is doing."