Liam Chilvers, Anthony Griffith and Rob Taylor have been released by Port Vale, while a dozen players have been offered new contracts.
Adams, whose own contract situation with the Sky Bet League 1 club has yet to be resolved, made public his retained list on Friday morning.
Defender Chilvers, midfielder Griffith and the versatile Taylor all leave Vale Park along with Chris Shuker, who this week announced his retirement due to an ongoing knee injury.
"I would like to wish Liam Chilvers, Rob Taylor, Chris Shuker and Anthony Griffith the very best of luck in their future careers and thank them for their service whilst at Port Vale," said Adams.
Chris Neal, Carl Dickinson, Doug Loft, Jennison Myrie-Williams, Joe Davis, Chris Lines, Ryan Lloyd, Richard Duffy, Chris Birchall and Billy Knott have been offered new contracts.
Meanwhile, Chris Robertson, Louis Dodds, Gavin Tomlin, Tom Pope, Sam Johnson, Ben Williamson and Kaid Mohamed are still under contract.