The Potters, playing in major European competition for the first time in 37 years, took the lead in the third minute when Jon Walters was allowed space to nod in Matthew Etherington's measured cross.
The hosts controlled the third round qualifying first leg match for long spells thereafter and particularly in the first half, had several chances to extend their lead.
The second goal was not forthcoming, though, leaving the tie more finely poised than it might have been ahead of next Thursday's return leg in Croatia.
Pulis felt his players should have made more of the openings that came their way, but was pleased they did not concede an away goal.
"It was a great atmosphere and we won the game, but we were disappointed we didn't win it by more goals, especially given the first half," Pulis said.
"We had enough opportunities and chances to come in more than 1-0 up.
"But we've kept the clean sheet, which is important. We'll go to Split and if we score a goal, they will have to score three to beat us.
"It was a fantastic start and our sloppiest period was 10 or 15 minutes after we scored.
"Then we picked it up for the last 20 minutes of the first half and we could have scored three or four goals.
"It would have been no embarrassment to us if we had come in two or three up."
With still more than two weeks to go before the start of the Barclays Premier League season, it came as little surprise that Stoke looked increasingly weary as the game went on.
Pulis fielded a strong starting team and plans to do so again for the second leg - although he hopes he might have one or two more players to call on by that stage.
"We tired in the second half," Pulis said.
"There were four or five who really tired, including the wide players (Etherington and Jermaine Pennant) and Kenwyne Jones.
"At the moment with the injuries we have got and the fact that we haven't been able to bring anybody in, you are looking over at the bench and there wasn't a lot that we could have changed.
"Another time, if it had fallen right for us, we could have had (Achilles injury victim) Ricardo Fuller to bring on for 20 minutes and really livened the place up.
"We are looking to bring more players in and if we can do that, then brilliant."
Stoke's only summer signing to date, Jonathan Woodgate, was among the substitutes and although he deemed it too soon to throw the defender into action against Hajduk, Pulis was delighted with his contribution off the pitch.
"It was great to have him on the bench and he has been brilliant around the dressing room before the game - his attitude has been fantastic," Pulis said.
"He will be a great help to the younger players. We have quite a young side - if you look at the back four tonight, it was very young, with a young goalkeeper, so we need experience there."
Hajduk boss Krasimir Balakov praised his players' efforts in ensuring it is all to play for in Split next week.
"We still have the second half to play - every match has got two halves," Balakov said.
"I felt the match actually went very well, particularly in the second half.
"You have to get used to the dynamic and I feel the players did extremely well."