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.
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."