The Potters travel to London on Monday night to take on Allardyce’s men, who occupy seventh position in the Premier League.
The Hammers have been criticised for their direct style of play, but Pulis believes that the Upton Park outfit have been very impressive:
“I don’t think he (Allardyce) pays too much attention to what people do or do not think.” He told SkySports.
“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 achieved promotion with Bolton during 2001 and kept the Trotters in the top-tier until he left in 2007.
After a short spell with Newcastle, he took charge of Blackburn guiding them away from relegation before getting sacked.
Pulis believes that Allardyce does not get the recognition he has earned during his career:
“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.”