The Bosnia and Herzegovina international was overlooked at the PFA awards on Sunday night as Manchester United's David de Gea was selected in the team of the year.
"I think he has been consistently the best goalkeeper in the Premier League this season," Pulis is quoted as saying by Sky Sports News.
"He's been different class for us. I think the experience he's got from playing games regularly has been the biggest factor.
"Asmir has had a full run at the team this season and grown in stature because of it."
Begovic joined Stoke from Portsmouth in February 2010 for just over £3m.