Although they have made progress in the cup, it has been a generally miserable season so far for the Hammers, who have taken just six points from their opening nine games.
The London outfit have won only one of those fixtures, but Pulis feels there is quality within Avram Grant's squad and, although likely to make several changes to his own starting line-up this evening, the Potters boss will not be taking the assignment at Upton Park lightly.
"Although we will make one or two changes, we will go there and try to win the game," Pulis told the club's official website.
"It will be tough because, despite their current position, they have some quality players and we must respect that."
One player that looks set to make Pulis' starting XI, as he has done in the previous rounds, is Tuncay Sanli.
Tuncay has not started any other games for Stoke this season, but came off the bench on Sunday against Manchester United at the Britannia Stadium and netted a sublime 81st-minute equaliser before Javier Hernandez's second goal of the contest sealed a 2-1 victory for the visitors.
Pulis has played down talk of a rift with the Turkey international - who was reported to have left in a taxi prior to kick-off after being omitted from the squad that faced Bolton earlier this month - but has challenged him to build upon his impressive cameo at the weekend.
"It was a great goal when we needed a bit of inspiration," Pulis said.
"He can produce things like that, but he needs to do that more often for us.
"People have asked me if there is a problem with Tunny - there isn't.
"He's as good as gold and he's a great lad to have around the place."