The Irish international missed from the spot during Saturday's 1-0 defeat to Fulham, which was his fourth failure from 12 yards in his last 10 attempts.
However, Pulis has insisted that it will be up to the player himself if he is to take the next one that the Potters are awarded.
"If Walts wants to step up and take the penalty, that's up to him," Pulis told The Sentinel. "I've never been one to stop them taking them if they want to and I'm sure he'll have the confidence to take it."
Walters joined Stoke from Championship side Ipswich Town in 2010.