The Stoke City midfielder was charged on Monday after appearing to stamp on the leg of Arsenal's Olivier Giroud during last weekend's Premier League meeting, and subsequently received a three-match suspension.
Though the incident went unpunished during the match, it was caught on video.
Stoke immediately launched an appeal after the charge was brought against Adam, claiming there was no intent to harm Giroud.
However, an FA Independent Regulatory Commission upheld the original ruling, meaning Stoke manager Hughes will be without the Scotland international for fixtures against Norwich City, West Ham and Aston Villa.
Stoke chief executive Tony Scholes has already voiced his disapproval on the decision and hinted at FA bias by stating: "(I am) not surprised because clubs like ours very rarely succeed in appeals to the FA."
Hughes has also aired his grievance, and believes Adam was subjected to "trial by media".
"I think the process is fundamentally flawed," said Hughes.
"If the game was reviewed by the people who were actually there on the day, immediately after the game, then any decision after that in terms of possible incidents missed in the game you would accept there was maybe something to investigate.
"The people involved knew the context of the game rather than allowing trial by media.
"By the time the decision (to ban Adam) was made on the Wednesday I think the agenda was set.
"We went through the process because we felt so strongly about it but we felt there was so little chance of it being successful because of the process.
"It has to be preferable to asking three referees, who are probably doing something else, to come together and review something out of context and make a decision based on what they see.
"As soon as the referee says he has not seen the incident - which we have a view on - then it goes to the panel but I just think when the game is taken out of context and it is slowed down to the 'nth' degree it can look worse than it is.
"The annoying thing is we can never question a referee's integrity - and we wouldn't - but when we get the written report back it questioned the integrity of my player. They can't have it two ways."
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