Brighton ended Hughton's four-and-a-half year reign last Monday, the day after his side's 4-1 defeat by Manchester City meant they ended the season in 17th spot.
"I was hugely disappointed and surprised, by the decision that was made to end my time with Brighton and Hove Albion FC," Hughton said in a statement from the League Manager's Association on Wednesday.
"I thoroughly enjoyed my four and a half years managing this special football club. I would like to put on record my gratitude to my coaching staff, the players, fans, everyone connected to the club and the wider community of Brighton and wish them luck for the future."
Hughton led Brighton into the top flight in 2017, ending a 34-year absence, and they survived a second season despite failing to win any of their last nine games.
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Brighton also reached this season's FA Cup semi-final.
LMA chief executive Richard Bevan said Hughton's tenure had been inspirational.
"He helped transform Brighton & Hove Albion, from fighting relegation to League One, to competing with the best teams in the world and retaining Premier League status for yet another season," he said.
"He continues to be a tremendous role model for young managers and coaches in the game."
Brighton named former Swansea City boss Graham Potter as their new manager this week.
(Reporting by Martyn Herman; Editing by Amlan Chakraborty)
