Birmingham City have confirmed the departures of assistant manager Terry McDermott and first-team coach Derek Fazackerley by mutual consent.
The club had made no comment, for legal reasons, since Clark admitted the pair had left his backroom staff last week.
But Birmingham made a statement on their official website on Friday.
"We all decided that it was in the best interests of all parties for Terry and Derek to part ways from the football club," said Clark.
McDermott and Fazackerley, both 62, were brought to St Andrew's by Clark when he became Birmingham manager in June 2012, and both were missing from the dug-out for last Saturday's 2-1 win at Blackpool.
Clark was unable to go into too much detail last week, but insisted the departed duo had not been sacked - while the club have now said that the move was not down to cost-cutting measures.
"This certainly wasn't a decision imposed by the board, who have been very supportive, but a conclusion Terry, Derek and I reached following discussions," said Clark.
"I have known Terry and Derek for many years and they both remain good friends. I would like to take this opportunity to thank them for their loyalty, friendship and work ethic during my time as a manager with both Huddersfield Town and Birmingham City."
Former England international McDermott, a three-time European Cup winner with Liverpool as a player, and Fazackerley, who worked alongside Kevin Keegan when he was in charge of England, were part of the backroom set-up at Newcastle during Clark's playing days in the north-east.
McDermott became assistant boss at Huddersfield when Clark was appointed manager in December 2008, with Fazackerley also joining as first-team coach before linking up with Leicester less than two years later.
Clark and McDermott were sacked by Huddersfield in January 2012, but the trio were reunited when the former Newcastle midfielder was given the Birmingham job later that year.
The existing backroom team of Steve Watson, Richard Beale and John Vaughan, who were on the bench at Blackpool, are to remain at the club as they attempt to improve on Blues' position of 16th in the Championship.
Meanwhile, Birmingham have confirmed that former Crystal Palace defender Darcy Blake, a free agent looking for a new club after exiting Selhurst Park on transfer deadline day last month, is at St Andrew's on trial.