Stoke showed their mettle in recovering from a 4-0 drubbing by Liverpool at Anfield in midweek but Pulis was disappointed not to secure a second win of the campaign.
The Potters had to make an early change as striker James Beattie left the field with a knee injury having fallen awkwardly in a challenge with Blues' goalkeeper Joe Hart.
Dave Kitson came on and mustered some half-chances for himself, glancing a couple of headers wide of the mark.
But it was Ricardo Fuller who will rue the best of the missed chances as he headed over from six yards out and toe-poked an effort wide.
He said: "We are disappointed not to get three points. Our big worry at the start of the season was our first three games.
"When you play one of the top four, as we did at Liverpool in the week, it saps your energy because you have to work so hard to live with them.
"It was great to keep a clean sheet after conceding four at Anfield. It was a good response. We needed Thomas Sorensen to dig us out of trouble with a great save but we still feel we could have won the game.
"I think we created enough, I think when Ricardo, late on, when he's got around the back and then he toe-pokes it behind, I think that's a great chance.
"If he plays it back or plays it across goal then you'll get (Dave) Kitson coming in or their defence to pop it in.
"So there was a lot of opportunities that we had that with a little bit more calm they would've turned into goals."
Pulis confirmed Beattie's injury was not as bad as first feared and he will be fit for the next Premier League game against Sunderland on Saturday.
Meanwhile, Birmingham boss Alex McLeish insists the proposed takeover by Carson Yeung is not causing uncertainty on the playing side as his team took their points tally to four from the opening three games.
He said: "Does the takeover affect players? I don't think so. We've got a spirit in the dressing room we've cultivated and harnessed over the last season and a half.
"Other people have talked about it (the takeover) but, regardless of what happens with the club, the players have a lot of belief in themselves and I am pleased with their start to the season.
"I'd have liked to have had six points or maybe even more but we won't be too greedy and I know the season is going to be long and tough."
McLeish was pleased with the way his side eventually got to grips with controlling the threat posed by Stoke's long-throw expert Rory Delap.
He said: "Every time the ball goes out in those areas, Stoke fans almost suck the ball into the net and they really get behind their team.
"But it was important we didn't panic. In the first half we didn't deal with it as well as we did in training but in the second half I didn't feel it was a massive threat to us.
"I don't think we are too disappointed with a point. In the second half we made chances which ignited us a little bit and I thought if we were going to win the game it was going to be in that period.
"We got good control in the midfield but Stoke are always dangerous on the break and make if difficult for you to score and I am not unhappy about the point."
McLeish confirmed that he is still trying to sign Sporting Gijon midfielder Michel which could be the last deal approved by the current board if Yeung takes control within the next month.