In a game of few chances, Palace dug deep to clinch a point and frustrate their relegation rivals at the Stadium of Light to remain out of the bottom three.
And Pulis was quick to point out how important it was for Palace to leave the north east with a share of the spoils.
"It was a must-not-lose game for us," said Pulis.
"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."
Pulis felt his players reacted well in front of a boisterous set of Sunderland supporters.
The Welshman added: "There is half-a-dozen players who have not played at the Stadium of Light, so coming here, (Sunderland head coach) Gus (Poyet) had wound the supporters up, I thought they were really behind their team 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."
Having presided over an upturn in fortunes since taking charge, Pulis has reiterated that Palace are capable of staying in the Premier League.
"It is a situation where we have to try and get as many points as we possibly can, we are in the frame with 10 other teams, it is remarkable really how many teams are down there and how many teams are involved," he said.
"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 10 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."
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