Marouane Chamakh's header earned a 1-0 win over West Ham as Palace moved off the foot of the Premier League table.
"It's a great result and we have to put points on the board to give everybody hope," said the former Stoke manager.
"The fans were wonderful, but you have to win these games to give them the opportunity to do what I've come here to do, which is keep the club up."
A second win in three games gives Pulis a chance of maintaining his 21-year record of never being relegated.
Palace are now above Sunderland in the table but are still in the relegation zone and face a crucial game against fourth-from-bottom Cardiff on Saturday.
Pulis praised his side's "unbelievable" work-rate and highlighted the efforts of goalscorer Chamakh and fellow striker Cameron Jerome.
"In the first 20 minutes, we were on the back foot, we gave the ball away sloppily and looked pretty nervous, but then we gradually got into the game and we scored a good goal," he said.
"I'm very pleased for Chamakh, who has really worked hard since I came in the door. He and Cameron Jerome looked a handful.
"For all of West Ham's possession, I think we most probably created the more clear-cut chances."
Pulis added that the win would improve morale within the team.
"We need to win our home games, so to get off to that sort of start is brilliant, but everybody has put a shift in," he said.
"We lacked a bit of quality at times, but we know that, so they have to work even harder when we don't have the ball."
Pulis hinted he might have funds to spend on new players when the transfer window opens in January.
"If we can stay in touch with the rest of the group and we can can get a couple in - and we have to do that within the restrictions of the football club, I understand that - then that will give us another lift which we will need for the second half of the season," he said
West Ham manager Sam Allardyce was unhappy with his side's marking for Palace's goal.
"That's the most disappointing thing for me because that's lost us the game effectively," he said.
"On such a crucial game, we should not have let that slip. A point at the end of the day wouldn't have been a bad result. It's all our fault."
Palace's upcoming fixtures
- 7 December: Cardiff (home)
- 14 December: Chelsea (away)
- 21 December: Newcastle (h)
- 26 December: Aston Villa (a)
- 28 December: Manchester City (a)