Huth will serve a three-game ban having opted not to contest a violent conduct charge brought against him this week by the Football Association.
The incident - missed by match officials at the time - saw the German catch Cottagers defender Philippe Senderos in the face with his forearm.
Asked about the matter on Thursday morning, Pulis, who recruited Huth for Stoke from Middlesbrough in 2009, said: "Robert has been fantastic for this football club - a great player and one of the signings we will look back on and say 'what a wonderful signing'.
"But I think he has let himself down more than anything else.
"I don't think Robert will be pleased with it, and it affects the team.
"But everyone makes mistakes, and he will be big enough and strong enough to hold his hand up and say that what he did was wrong."
Either Marc Wilson or Geoff Cameron, both of whom usually play at full-back for Stoke, are set to cover for Huth in the middle in Saturday's home league clash with West Ham.
A specialist centre-back who is no longer an option for the Potters is Matthew Upson after he joined npower Championship side Brighton in January on loan until the end of the season.
Pulis has stressed it was difficult to prevent 33-year-old Upson 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."
Midfielder Steven Nzonzi will be wearing a protective face mask if he features against West Ham after he broke his nose in the Fulham match - the result of a collision with Dimitar Berbatov.
Appearing wound up, Nzonzi subsequently made a gesture to the home fans and was then booked for putting his hand in Bryan Ruiz's face - actions Pulis does not condone, but regards as more understandable than what Huth did.
"The reaction wasn't good, but there was a reason why the reaction wasn't good and that is most probably the difference between Robert and Steven," Pulis said.
"When you get a smack in the face like that, there is going to be a reaction, it is a natural thing. You shouldn't do it, but it is natural.
"But with Robert, I don't know what he was up to, to be honest."
Pulis has also confirmed that striker Michael Owen (thigh) and winger Matthew Etherington, who came off against Fulham due to a back problem, will undergo late fitness tests ahead of Saturday's game, with the latter believed to have the better chance of being involved.