The England winger retaliated after Stoke's Rory Delap kicked the ball at him after the whistle had blown in the Potters' recent 1-0 win at the Britannia Stadium.
Referee Mark Atkinson did not see the 27-year-old lash out but, after studying television replays after the game, he stated that had he seen the incident he would have sent the former Chelsea man off.
The result means that Hughes will be without Wright-Phillips for the next three league games against Portsmouth, Liverpool and West Ham, all of which are away from home.
"We admitted at the time that there was a reaction but there were reasons why Shaun reacted like he did," he told the club's official website.
"We hoped that there would have been a little bit of leeway where the decision makers were concerned, but unfortunately I think the FA has to go by the letter of the law.
"They will support the referee's report, so unfortunately we will miss Shaun for the same length of time that Stoke will be without Rory Delap.
Harsh"That does not seem correct in my view, but that's where we are. There will always be grey areas open to debate, but I just think Shaun's case should have been judged on its own merits.
"Shaun has been really hard done by because of the severity of the punishment.
"It's a blow because he has been playing really well, he has such a positive impact, and his work rate is such that he always causes a threat to teams.
"But there is nothing we can do now, we just have to get on with it."
Meanwhile, City have cut the prices of season tickets for the 2009/10 season in a bid to help fans through the current economic crisis.
On average the season tickets have been cut by seven per cent and fans will be given an extra three months to come up with the money.
"Our season card-holders are the cornerstone of this club and since our arriving here, we have listened to their feedback and their concerns on a great range of issues," chairman Khaldoon Al Mubarak said.
"By pushing back the date for season-card renewals we hope to make some small difference to the supporters who follow the team every week.
"We have also sought to respond to fans' concerns on pricing and hope that the price freezes in some areas and discount in most areas of the ground will be welcomed."