Shaun Wright-Phillips insists he is happy again at QPR after turning down "offers and opportunities" to move in January.
Blackburn goalkeeper Paul Robinson has told Sky Sports he will leave the club this summer and could move abroad.
Interim boss Neil Adams, who the board say is a candidate for the permanent vacancy at Carrow Road after doing "an admirable job in difficult circumstances", replaced Chris Hughton last month but could not turn things around.
A statement published on canaries.co.uk read: "Everyone at Norwich City shares our fans' deep disappointment that we have been unable to secure Premier League status for a fourth consecutive season, despite the best efforts of players and staff at Carrow Road and Colney.
"We'd like to thank our fantastic supporters for their unswerving and passionate backing home and away in what has been a very challenging season for everyone connected with Norwich City. As always, the 'Yellow Army' has been a credit to their Football Club and to the county of Norfolk.
"The Board fully accepts that mistakes have been made which have contributed to our relegation.
"It is always our stated strategy to improve the squad in every transfer window. We backed the manager with the funds to sign a number of players this season with every intention of improving the squad, but unfortunately that improvement did not materialise."
Before the start of the season Hughton embarked on a busy summer of transfer activity, bringing in the likes of Gary Hooper, Leroy Fer, Martin Olsson and Nathan Redmond. But it was the failure of big-money signing Ricky van Wolfswinkel to settle - scoring just one league goal all season - which stood out most glaringly.
The statement continued: "Work is already under way to learn from the experiences of this season and to prepare for a busy summer as we focus all of our energies and resources on competing in the Sky Bet Championship next season.
"The next step is to confirm who will be our manager next season and this process is under way now.
"Neil Adams, who has done an admirable job in difficult circumstances, is one of a number of candidates the Board is talking to.
"The Board will confirm who our manager will be in the 2014-15 season in a statement to supporters within a week."
Former Cardiff and Watford manager Malky Mackay has been linked to the Norfolk club while another ex-Hornets boss, Gianfranco Zola, remains available for work in England following his December resignation at Vicarage Road.