Pulis took over at Selhurst Park last week, having been in the stands to watch Palace pick up three points courtesy of a 1-0 over Hull City at the KC Stadium.
However, his first game in charge of the club saw them beaten 1-0 by Norwich City on Saturday, Gary Hooper striking half an hour in at Carrow Road.
The defeat keeps Palace bottom of the Premier League ahead of their first tie with West Ham in the top flight since 1998, although Pulis was pleased with the way his side performed in Saturday's defeat.
"There are certain clubs in the Premier League that we can't compete with and then there are others who you have to compete with," he said.
"When you play those teams you have to make sure you are on it and (on Saturday) we have come away from home and done exactly that."
Palace have a strong record against Tuesday's opponents, especially at home.
The last time Palace were beaten by West Ham on home turf was in 1991, although Sam Allardyce's men come into the game having lost just twice on the road in the top flight this season.
West Ham will have been buoyed by a London derby victory over Fulham on Saturday, securing a 3-0 win thanks to second-half goals from Mohamed Diame, Carlton Cole and Joe Cole.
Pulis will be without the suspended Yannick Bolasie, while long-term absentees Jack Hunt (ankle) and Glenn Murray (knee) remain unavailable for Palace, while the game is likely to come too soon for Adlene Guedioura, who has a rib injury.
Allardyce has been handed a boost with the expected return to training of Andy Carroll, who has not played for the club this season, although the England man is unlikely to feature until the new year.
Carlton Cole's goal on Saturday was his first for West Ham since December 2012, and he may be eyeing a spot in the starting XI, but there will be no place for Winston Reid (ankle) or Ricardo Vaz Te (shoulder).
Mladen Petric and Razvan Rat could be pushing for involvement after calf and hamstring injuries respectively.
