Pulis started with former England team-mates Michael Owen and Peter Crouch in attack but it was npower Championship side Palace who looked most likely to break the deadlock.
Owen started his first match in 14 months at the ground where he scored on his Liverpool debut as a 17-year-old against Wimbledon in 1997. But, 16 years on, Owen did not manage an effort on target and lasted just 53 minutes.
Owen and Crouch were playing together for the first time since both came on as half-time substitutes for England in a 1-0 defeat by France in 2008.
And the old partnership could have given Stoke the lead in the 12th minute when Owen got his head to a corner. The ball looped across goal but Crouch could only direct it wide from all of six yards out.
Crouch had another chance when Ryan Shotton found him with a curling cross but this time his header flew over the bar.
Pulis said: "When the draw was made we knew this would be a very tough fixture - especially away from home.
"We have just come off the back of four very tough Premier League games. This is a tough ground to come to and they are a top Championship side.
"They played really well. They've got some dangerous players in their team and we are pleased with the result. They are a good side, Ian Holloway's got them well-motivated and it was always going to be difficult.
"I was bringing on players like Kenwyne Jones, Cameron Jerome and Charlie Adam to try to win the game. But both teams are in the draw so that's something to look forward to."