“I do hope that the club remain focussed on youth development”
The 65-times capped Scotland defender later told BBC Scotland he felt his most recent tenure at the club should be considered a success.
"Part of that role for the last eight years has been setting up the development programme, and in the last year I've been working at it seven days a week," he said.
"I think, looking from the outside, most commentators would say the young players coming through have been of a high quality and in good numbers.
"So from that point of view, I hope that everyone would agree that that role has been a very successful one.
"[I was] really surprised to hear the chairman say that that role is no longer needed at the club and disappointed because there's still a lot of work to be done in that department to make sure that the club maintains that conveyor belt of talent and produces these players for the first team.
Chairman Stewart Milne on the changes at Pittodrie
"I do hope the changes won't derail that in any way. I do hope that the club remain focussed on youth development and don't just pay it lip service because it's too important for that to happen.
"It has taken eight years to get where it is and it can be dismantled in a very short time."
Miller remained supportive of the club, manager Craig Brown and assistant Archie Knox while pointing to his own role in helping develop the Scottish Premier League outfit's youth system.
He said he "would like to thank the club, the fans and all the staff for their support during my long association with the Dons.
"I would like to wish Craig and Archie and all the football staff and players good fortune for the new season.
Spent entire playing career at Aberdeen as a defender, joining in 1972
Won three league titles and seven cups
Captained club to European Cup Winners' Cup and European Super Cup wins in 1983
Won 65 Scotland caps
Retired from playing in 1990
Became Aberdeen manager in 1992 but was sacked three years later
Rejoined club as director in 2004
"I must also extend my gratitude to all my development colleagues who helped put in place our successful youth development programme, which, after eight years of tireless effort, has produced a number of exciting talents now in the first-team squad.
"These youngsters and the bright crop coming through are the future of the club.
"It goes without saying that I have enjoyed every minute of my time as a player, captain, manager and director of the club and I will now continue my association as a supporter and will continue to have the best interests of the club at heart.
"I am leaving the club on good terms and wish the club all the best.
"I will take a little bit of time to reflect. I've been involved in the game for a long time and I would hope to continue in the game if the opportunity arose."
Aberdeen had announced a year ago that Miller's role at the club had been "redefined", with new chief executive Duncan Fraser having taken over first-team duties, such as contracts, from the former Scotland defender.
Now, four other directors - Martin Gilbert, Hugh Little, Ken Matheson and Chris Gavin - are departing along with Miller.
Businessman George Yule has been appointed to the new role of executive vice-chairman.
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