Hughton, 60, who guided the Seagulls to promotion to the Premier League in 2017, departed the club the day after their final game of a season in which they finished 17th, two points ahead of third-bottom Cardiff.
"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 released by the League Managers Association.
"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 & Hove and wish them luck for the future."
The LMA said Hughton had been an inspiration for helping turn Brighton's fortunes around during his time at the club.
"Chris' impressive tenure has been inspirational for his peers in the game," said LMA chief executive Richard Bevan.
"He has 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.
"This season, he again proved his managerial ability in also leading his team to the semi-final of the FA Cup for only the second time in the club's history.
"He continues to be a tremendous role model for young managers and coaches in the game."
Hughton, who has been replaced by Graham Potter, was appointed by Brighton in December 2014 and led them to promotion after they finished second in the Sky Bet Championship behind Newcastle at the end of the 2016/17 season.
The Seagulls finished 15th in their first campaign in the Premier League and one place above the relegation zone this season after winning just three of their last 23 league games.
Brighton lost 1-0 to eventual winners Manchester City in the FA Cup semi-finals.
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