Bradley Johnson's headed goal at the end of the first half proved enough to secure the Canaries a second successive Barclays Premier League home win.
Pulis, though, was left less than impressed by the award of the initial free-kick for a foul by full-back Andy Wilkinson on Robert Snodgrass out on the far touchline, and also referee Andre Marriner ruling midfielder Charlie Adam had dived earlier in the first half.
"The goal was a disappointment. I have been in to see the referee to have a quick chat," said Pulis.
"I thought it certainly was not a free-kick, and the disappointing thing is when the lad falls, Andre and the linesman are so close to it.
"He has booked Charlie in the first half for diving - I have just had a look at that and [Javier] Garrido pushes him in the back, so that is a double kick in the teeth when he gets both those decisions wrong and even worse when they score from it."
Diving has become a contentious issue in the English game, and Pulis believed retrospective punishment is the way forwards.
He added: "Referees give the decisions they see on the day, and he has seen it differently to what we have. When he sees it again on the telly tonight [Saturday], he will have a different opinion.
"I think the [diving] situation should be taken completely out of the hands of the referees and it should be retrospective on a Monday, there should be a panel which sits to decide whether a player has dived or not, that eases the pressure on referees and they only make that decision if they are 110% certain someone has cheated."
Norwich manager Chris Hughton defended Snodgrass against any accusations of unsportsmanlike conduct.
He said: "I have not seen it since, but I have heard the comments.
"If anything is labelled at Robert Snodgrass, then you have got to say the same about Charlie Adam, who went down.
"If you are looking at incidents in the game, there are so many and you are always going to pick out a few, but it is a tough physical game and you have to be able to deal with it."
Stoke had won just once in the league before Saturday afternoon, drawing six.
The visitors certainly had enough possession in the second half, when they carved out good openings for first Jonathan Walters, whose close-range shot was blocked, and then from substitute Kenwyne Jones.
"[Goalkeeper] Asmir [Begovic] did not really have many saves to make and in the second half, I thought we played like the home team," said Pulis.
"We had the two best chances of the game, and they have got to be scored.
"It is disappointing to come away with nothing."
Norwich, meanwhile, are now four games unbeaten in all competitions following the international break, having reached the quarter-finals of the Capital One Cup with victory over Tottenham in midweek.
Hughton, though, accepted the Canaries could have given themselves more breathing space during the closing stages of Saturday afternoon, when the hosts soaked up plenty of pressure.
"You cannot be too disappointed when you have won the game, but we could have made life better for ourselves," he said.
"We needed to put a little more pressure on them, we could have done better when we had the ball and had two very good chances apart from scoring the goal.
"We should have pressed more, but that takes a lot of energy, especially when you are playing against a team like Stoke.
"But I thought we dealt with it very well and apart from Kenwyne Jones' header we restricted them to a couple of half-chances."