Media playback is not supported on this device
Potters boss Mark Hughes confirmed Berahino, who joined the Potters in January, had served an eight-week suspension when he was at West Brom.
His comments follow newspaper reports Berahino was banned after failing an out-of-competition drugs test.
"Anything Stoke asked for, we told them the truth," Pulis told BBC WM Sport.
"We never picked him again because his fitness levels, mental levels, were never what we wanted.
"This club has been absolutely fantastic towards Saido. The way it's protected him, the way it's looked after him. He should be really, really grateful."
The 23-year-old is set to return to the Hawthorns with Stoke in the Premier League on Saturday.
Asked whether Hughes was the man to help Berahino, Pulis said: "Personally, I don't give a damn now.
"I've spent two and a half years at this club and he's not my problem anymore. I wish him all the best."
Pulis would not comment on the nature of the ban because it was a "personal issue", but he said Berahino never returned to the form he produced before West Brom rejected a bid from Tottenham for the striker in August 2015.
"Saido was very good the first six months I was at this club," said the Welshman. "He didn't go to Tottenham, and from that point on it's been a real struggle in every way, shape and form."
BBC Sport contacted Berahino's representative for comment, but has received no reply. The FA does not comment on its social drugs policy regulations.
West Brom boss Tony Pulis says he does not "give a damn" about Saido Berahino's future because the Stoke City striker is no longer his problem.