Following Wednesday's surprise 3-2 win at Everton, Palace boss Pulis said he believes his side's 10-point cushion over the bottom three with just four games remaining means their top-flight survival is secure.
Pulis has built a reputation as a manager who expects nothing less than 100 per cent from his players, though, and despite their comfortable position in the table, he is demanding his charges do not rest on their laurels between now and the end of the season.
"We have a responsibility to the Premier League to turn up for the next four games," the former Stoke City manager told Sky Sports.
"I have got great respect for Sam (Allardyce) and West Ham United and then we have got what could be big games against (Manchester) City and Liverpool.
"I have said to them that it is a fantastic achievement but we have a responsibility to perform in the next four games."
The victory at Goodison Park was Palace's fourth in succession, lifting them to 11th place and above Saturday's opponents in the standings.
West Ham, like Palace, have climbed away from peril since the turn of the year, with four wins on the bounce in February moving them into mid-table.
They have fared less well since then, however, with a run of two wins and five defeats in their last seven matches leaving them in 12th place, seven points above the drop zone.
West Ham's home form has been strong over the last two months, winning four out of six games, and manager Allardyce will be keen to improve on that record on Saturday and secure three points that should calm any lingering relegation fears.
They, too, were in action in midweek, going down 3-1 at Arsenal despite taking the lead through Matt Jarvis, and the Upton Park faithful know a return to winning ways on Saturday will see them climb above their opponents and further aid their bid for a top-half finish.
Captain Kevin Nolan missed the trip to the Emirates Stadium with a hamstring problem and is a doubt for Saturday, as are James Collins (calf) and Joey O'Brien (shoulder).
Palace's only doubt is Kagisho Dikgacoi, who missed the game on Wednesday with a knock.
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