Ajax technical director Danny Blind and the club's board resigned on Thursday following the row over the blocked appointment of Louis van Gaal as general manager of the Dutch footballing giants.
Ajax legend Johan Cruyff last week won his legal battle to prevent the appointment of van Gaal which had been made by the club's Council of Commissioners without consulting him - although he is one of the five board members.
"I have a clear vision of Ajax's future and van Gaal's arrival is part of that," said Blind.
"Now that his arrival is no longer the case I can't and don't want to continue."
Both van Gaal and Cruyff are former Ajax coaches and have clashed in the past.
Cruyff took legal action to block his countryman's appointment and was backed by 15 coaches from the club's training centre.
Cruyff, 64, had restructured the club in recent years by giving more power to former plays such as Blind, Frank De Boer and Dennis Bergkamp, who are coaches, with Wim Jonk responsible for training.
"The coaches from the training centre are all former club players. I've always been 200percent behind this project and I maintain that it's very important for the club," said Cruyff, who feared that Van Gaal would dismantle his work.
Van Gaal, 60, had been due to work alongside Blind and commercial director Martin Sturkenboom as part of a new leadership structure at the home of the four-time European champions.
The former Bayern Munich coach managed Ajax between 1991 and 1997, notably leading them to the Champions League title in 1995, and was sporting director from 2003 to 2004.