The 55-year-old was dismissed from his post as manager following Saturday's 1-0 home defeat to West Brom, a loss that leaves the Carrow Road club just five points above the relegation zone.
The timing of the club's decision was criticised in some quarters, with Norwich having just five games left to preserve their top-flight status.
Hughton was active in the pre-season transfer window but claimed just eight wins from 33 league games in charge this term, though he insists Norwich's future was safe in his hands despite the unrest of the fans.
"I am naturally very disappointed to have lost my job but immensely proud to have served as Norwich City's manager," Hughton said in a statement released on his behalf by the League Managers Association.
"I understand the recent frustrations, but I remained totally confident that we were on course to create history at the club by retaining our top-flight status and move into a fourth consecutive season in the Barclays Premier League.
"Collectively we were ready for the challenge that the final five games presented and we believed we would reward the club and the supporters by achieving that objective.
"Over the last two seasons many new players arrived at the club and it has been a period of transition, but I would like to put on record that the commitment and work ethic shown by them, together with the players still retained from when I was appointed, has been exceptional. The same applies to my coaching and backroom staff whose contribution has been immense.
"I now wish to reflect before preparing for the next challenge. However, what goes without saying is that I sincerely wish everyone connected to the club, from the owners and the board through to the supporters who are the essence of every club, all the very best for the rest of this season and into the future.
"Norwich City is a great club and I feel honoured to have had the privilege of being its manager."
City travel to Fulham on Saturday for a crunch clash in the relegation battle; defeat would see Neil Adams' side slip to within two points of the drop zone, with matches against Liverpool, Manchester United, Chelsea and Arsenal still to come.
