In a contest of few clear-cut chances, the hosts posed the greater attacking threat but were unable to make a breakthrough and once again had to settle for a point.
Reflecting on his team's performance, Pulis said: "We went to win the game.
"We needed a break. I've just looked at a few of the set-plays in the first half and how two of them stay out, I just don't know.
"That is what you need - a bit of luck.
"It was always going to be a tight game. They are a good side - we certainly don't look down our noses at Sunderland.
"(Sunderland manager) Martin O'Neill has bought some quality players and they are a tough team to play against. But I thought there was only one team that would win the game, and that was us."