Pulis travelled back from south Wales after spending the day with family following the death of his mother earlier in the day, arriving just after kick-off.
However, he did not take his place on the touchline until the second half, when his side were already losing, but witnessed a character-filled comeback with goals inside the last 10 minutes from home debutant Kenwyne Jones and Robert Huth.
"I thought he'd have to come and have his say," Delap told Radio Five Live. "I don't think anyone was too surprised he turned up because everyone knows the character of the man.
"We should be able to do without him but great credit to him for turning up. I think the half-time talk was what we needed.
"That's why these people are successful managers. He knows when to say the right things and what to say and that was the case last night. I think it showed he proved his point in the way we played in the second half.''
"He's not the first to give the lads a lashing at half-time and he won't be the last. Sometimes it's the kick up the backside you need. He swore a lot but he always does - and he's not called me anything I've not heard before.''
The victory gave Stoke their first points of the season and former Republic of Ireland international Delap believes the result was significant.
"It was a must-win game - I think that's probably a big reason why he (Pulis) turned up and came into the dressing room at half-time," Delap said. "I think in the end we deserved the win - it should kick our season off now.''