The Scotland midfielder was charged with violent conduct after stamping on Arsenal striker Olivier Giroud in an off-the-ball incident at the Britannia Stadium last weekend.
Despite Adam protesting his innocence and being vigorously defended by Hughes and Stoke chief executive Tony Scholes, an independent panel upheld the charge and Adam must now serve a three-game ban.
Scholes said he was "not surprised because clubs like ours very rarely succeed in appeals to the FA" and Hughes has described the video review process as "fundamentally flawed".
The Potters boss also feels that Adam was subjected to a "trial by media" over the incident, which took the gloss off a priceless 1-0 win over the Gunners.
"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."
Earlier in the week, Scholes suggested the FA disciplinary committee were guilty of double standards after deciding that Manchester City's Yaya Toure had no case to answer despite appearing to kick Norwich's Ricky van Wolfswinkel in the back.
"Toure thought he would get a ban and did not for whatever reason," added Hughes.
"I don't really want to go into this territory (big teams v little teams) but it is difficult for everyone involved in the disciplinary process - we just want our concerns and voice to be heard sometimes.
"We have gone up against an outstanding team in Arsenal and played really well but come Monday the general view was we won because we kicked Arsenal off the pitch but that is totally not the case."
Meanwhile, Hughes insisted he will not be forced to change his transfer spending plans despite the club announcing losses of £31m earlier this week.
"I was made fully aware of the finances when I started the job and I accepted that wholeheartedly," he said.
"This was a great opportunity for me. The club is managed really well in the right manner and I'm sure those losses were able to be absorbed."