Palace were rarely troubled by Sunderland as the game at the Stadium of Light produced few chances.
Pulis admits that they could not afford to lose the game in the north east with the result keeping Palace three points ahead of Sunderland and the drop-zone.
"It was a must not lose game for us," Pulis said.
"We haven't got the quality of some clubs but the players have big hearts.
"Julian Speroni has had two proper saves to make and I am delighted with the players, they have given it everything and that is all I can ask.
"There is half-a-dozen players who have not played at the Stadium of Light, so coming here, Gus [Poyet] had wound the supporters up, I thought they were really behind their team today and shouted and screamed for every decision and every ball.
"They were very good so for them to withstand that and then I have just seen the chance [Kagisho] Dikgacoi missed late on and that was probably the best of the game."
Pulis insists that Palace are firmly focused on retaining their top-flight status.
He added: "It is a situation where we have to try and get as many points as we possibly can, we are in the frame with ten other teams, it is remarkable really how many teams are down there and how many teams are involved.
"It is just about keeping your head and making sure the players believe and if you lose games you have to bounce back.
"I know Gus said it was a must-win game for them, but with ten games left you can lose three and then win three in a row and you're almost there.
"I have been here before and I know how quickly things can change both for you and against."