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. I thought Sunderland defended really well and that their goalkeeper (Simon Mignolet) was outstanding. 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."
He added: "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. We are frustrated."
Stoke defender Marc Wilson sustained a serious-looking injury in a challenge with Sunderland striker Steven Fletcher only a few minutes into the second half and the Republic of Ireland international subsequently had to be carried off on a stretcher.
Asked for an update on Wilson's condition, Pulis said: "He has gone to hospital straight away, so we are just waiting for confirmation of what it is. We are not sure. I think he actually did it himself. I think his studs got caught in the ground."
Sunderland, who also registered their sixth league draw of the campaign, offered little going forward, although they did have a penalty appeal turned down in the second half when Fletcher's shot hit Robert Huth's arm in the box.
Giving his view on that incident, O'Neill said: "I've seen it back briefly. The truth is, I thought if it had been given against us, I might have been none too pleased. I think he has tried to keep his arm there, although if it misses him, it is in the net. I'm not sure it was a deliberate handball."
O'Neill declared himself satisfied enough overall with a point at the Britannia Stadium, although like Pulis, is keen to see his side start to chalk up a few more wins. "A point away from home isn't too bad. We have drawn a lot of games this season and we are just unable at the moment to turn one or two of those draws into victories," he said.
Source: PA
Source: PA