The midfielder joined Stoke towards the end of the summer transfer deadline from Liverpool.
However, Adam's international commitments with Scotland have meant that he has barely had a chance to train alongside his new teammates.
"He only watched us in training the day before the Wigan match and then he was off to play for Scotland straight after," said Pulis. "He hasn't even worked with us yet and that is really, really frustrating with him being a new signing.
"I know these players are top professionals, who can quickly adapt, but they are also playing against top professionals, so you want time with them on the training pitch to prepare.
"Hopefully, Charlie will come back to us fit and healthy on Thursday after his international commitments. I am sure I am not the only manager bemoaning the fact he has so many players away."
Stoke face champions Manchester City at the weekend.