The Scotland international was banned for three matches this week after an independent panel adjudged he was guilty of violent conduct for stamping on Olivier Giroud in Saturday's 1-0 win over Arsenal.
Potters chief executive Tony Scholes said he was "not surprised because clubs like ours very rarely succeed in appeals to the FA" and Hughes felt Adam had suffered from the incident not being assessed contemporaneously.
"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, because 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 had expressed his concern there appeared to be double standards at work after Manchester City's Yaya Toure escaped punishment for appearing to kick Norwich's Ricky van Wolfswinkel.
"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 it totally not the case."
Also this week Stoke posted financial results which showed a £31million loss.
However, Hughes said he was not concerned by that and it would not affect his transfer spending.
"I was made fully aware of the finances when I started the job (last summer) 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."
Stoke head to Norwich in the league on Saturday looking to improve on a woeful away record which has not seen them win outside of the Britannia Stadium since August.
"We are trying to address our away form. Our performance at Manchester City (1-0) where we were beaten by the odd goal shows we are improving," said the Potters boss.
"We've had more difficulty on our travels but we've spoken about what we need to do and winning these games (they also face West Ham, Aston Villa and Hull this month) is high on our list of priorities."