Boss backs Asmir Begovic to be top-class 'keeper
The two goals, both hit from outside the area by defender Chris Baird, proved too big a hurdle for Stoke, who created few chances, to overcome.
"We give them a two goal lead in the first ten minutes, and it's difficult then to chase the game," Pulis told reporters after the match.
"The start was very, very poor for us.
"We did really well at Blackburn and we really prepared the players, but like all human beings they let you down sometimes, or let themselves down.
"But after that first 20 minutes we got into the game. If we'd have got a goal it might have been a different game."
Despite the audacious nature of both of Baird's strikes, Pulis believed that goalkeeper Asmir Begovic should have tipped them both away. But the Welshman still has high hopes for the Bosnian, who has previously attracted the interest of Tottenham, Chelsea and Arsenal.
"I think Asmir will look at the goals and think he could have done better with both of them, even the first one," said Pulis.
"He can be a top, top goalkeeper and he can make saves like that. If I didn't think he could, I wouldn't be saying it - he'll be that good a goalkeeper."
The Welshman did not shake hands with his counterpart, Mark Hughes, after the game, and admitted that it was in response to his adversary failing to offer his hand after the two last met - a League Cup victory for Stoke that was marred by an injury sustained to Moussa Dembele as a result of a heavy Andy Wilkinson challenge.
"He's done it when we played in the League Cup," explained Pulis, "and I did it back but it's two Welshman with a bit of competition - it's nothing.
"He won't lose sleep over it, I'm sure he won't."