The Eagles go into the London derby at Selhurst Park in desperate need of points as they lie at the foot of the standings, six points from safety.
Palace have mustered just four of their current seven points at home this season.
"We have two games at home and we need to win our own games, there's no question about that," Pulis said in Monday's press conference.
"If we get the crowd behind us, which I don't doubt that, and we get some breaks, then we can do well.
"We are in desperate need of taking results to stay in the Premier League."
Tuesday's match will mark Pulis' first home game since taking over the London outfit last week.
"I'm looking forward to the atmosphere and being a local derby, it gives it a bit of spice," he said. "We need everything from everybody.
"We need this group to get together.
"We need to stay in the game if we can."
West Ham go into the match on the back of a 3-0 triumph over Fulham that lifted them to 15th place.
"Any game in the Premier League is a big game," Pulis said. "West Ham have some good players.
"They have been unlucky with (Andy) Carroll (out with a heel injury).
"They have a lot of experience in the Premier League and they have a well-balanced group of players.
"I don't think (West Ham) manager Sam (Allardyce) gets the credit he deserves.
"He is a top manager in the Premier League and he keeps succeeding in every club.
"At West Ham, he has stabilised the ship.
"We know it's going to be a tough game but we are hoping that we will get breaks."
Pulis will be hoping his side can show the same determination they displayed in the second half of Saturday's 1-0 at Norwich.
Despite the loss, the Welsh tactician was pleased with his troops.
"We did very well, especially in the second half," Pulis said.
"For an away performance, it was very good.
"We were unfortunate but that performance hopefully gives the players more confidence.
"When you are fighting against it, the lads have to go out and give it a go and I thought we did that.
"I knew it was going to be a tough job, I always knew that was going to be the case, a tough battle, we need to take our chances.
"That's what I told my players today.
"My players have the belief.
"I was pleased with what came out in that game.
"We just have to make sure we don't make certain mistakes.
"It will take me another couple of weeks to get my feet under the table.
"It's really about improving the team as quickly as we can."
Lack of goalscoring has been the Eagles' main weakness so far, they have found the net just four times in six home games.
Marouane Chamakh has found the net just once in 13 league appearances and Pulis expects a lot more from the Frenchman.
"Chamakh has to get in the box," Pulis said.
"Hopefully if he scores, then he will get a bit streaky as it happens with strikes and he can score a few goals."
The Eagles go into the encounter bolstered by the news that captain Mile Jedinak has signed a three-and-a-half year contract extension with the London outfit.
"We are very pleased," Pulis said. "We thought he was an outstanding team player.
"The time that I've been here, he has really impressed me.
"He is a real soldier and the lads respond to him.
"He has leadership qualities."