Apart from two Dirk Kuyt headers late in the second half the home side struggled to create chances.
But World Cup final official Howard Webb was called on to make some difficult calls with substitute Andy Carroll going to the floor on more than one occasion in tussles in the penalty area.
The South Yorkshire referee is by no means a favourite at Anfield and, although the Kop were unhappy with his decision-making, Pulis was not.
"I think it was more out of desperation," he said of the penalty appeals.
"Apart from Kuyt's effort - which he should have scored - I'm not saying Thomas Sorensen made save after save.
"They are a fantastic crowd here and they could see we were digging in and the players needed some help and by cheering the way they cheered every time ball went in there helped.
"Several referees might have buckled but thankfully Howard is strong and experienced enough to have not."
After their victory over Liverpool at the Britannia Stadium in September the result represented another success for Stoke.
"We are pleased with the effort and commitment of the players," said Pulis.
"They worked hard and that is four points off Liverpool and two clean sheets in the league and that is a great achievement."
Liverpool boss Kenny Dalglish would not be drawn on Webb's performance.
"It is difficult to understand when he talks to the players and explains something to them and then they commit the same crime immediately after it," he said.
"I think we have stopped trying to work out the logic of referees nowadays."
Dalglish was more concerned with the lack of chances created which contributed to a seventh draw in 11 home matches this season and led to them losing ground on fourth-placed Chelsea.
"They (Stoke) came to go away with a point and they got a point," added Dalglish.
"The responsibility was on us to be more imaginative and to break them down and we didn't manage to do it.
"The couple of opportunities we got we didn't take and in a game like that you have to take them.
"We looked pretty solid at the back - they had one shot in the first half and not much more after that - but it is our responsibility to break them down and on the day we just weren't good enough.
"There was nothing wrong with their effort of determination but on the day we were not good enough to break them down."
Dalglish employed the 3-4-2-1 formation which had won the game at home to Stoke last season but he said it was partly out of necessity.
"The personnel we had we didn't have much of a choice," he added.
"We left Daniel Agger out as a precaution, Jose Enrique had a bit of stomach virus so we were lucky to get him to play; we didn't have too many options.
"The boys at the back looked pretty comfortable - but they were only playing against one person."