With Huth unavailable, Pulis will have to use either Marc Wilson or Geoff Cameron, both of whom usually play at full-back for Stoke, in central defence against West Ham this weekend.
Upson was third choice before joining Championship side Brighton in January on loan until the end of the season.
But Pulis has stressed it was difficult to prevent the 33-year-old from moving on, and that Stoke had made attempts to bring in other defenders during the last transfer window.
"If I had had my way, Matty would have left 12 months earlier. There was an opportunity for him to leave (then) and he didn't go," Pulis said.
"Matty wanted to play football, he was absolutely desperate and is such a great pro.
"I have the greatest respect for Matty. He was fabulous at this football club and he had the opportunity of going to a club that have a chance of getting in the Premier League.
"We tried to get players in and it just didn't work."