Cole Stockton, Dylan Connolly, Ousmane Fane and Liam Gibson were already under contract while Arthur Gnahoua, Aaron Wildig and Adam Smith had 30 days to respond after being offered new deals.
However, Jonah Ayunga, Ryan Cooney, Ryan Delaney, Courtney Duffus, Wes McDonald, Ryan McLaughlin, Shane McLoughlin, Anthony O’Connor, Jon Obika and Connor Pye were all made available.
Pye’s inclusion raised a few eyebrows given the teenager had been praised by Adams’ predecessor, Stephen Robinson, and signed a first professional contract in January.
Adams said: “The problem we have got is 75 per cent of the budget has been taken up because of players in contract or renegotiating with players out of contract.
“We are in a difficult position at this moment in time because 75 per cent is a huge amount gone on players who haven’t been playing.
“Ryan Cooney, who we have made available for transfer, was the only player out of the 10 in the starting 11 for the last game against Sunderland.
“The difficulty for Connor Pye is he’s not going to find himself in my first-team squad.
“He’s got two years to run on a contract but, budget-wise, the circumstances are difficult.”
Also departing were Rhys Bennett, Toumani Diagouraga, Greg Leigh, Jacob Mensah and Freddie Price, all of whom were out of contract.
Adams had talked up Price’s potential during his first spell in charge but the 20-year-old only featured five times last season.
His involvement had been curtailed after a freak training ground injury last December saw a ball volleyed into his face.
That left him out for three months and unable to force his way back into the first-team picture upon his return.
“Freddie was a budgetary decision as well,” Adams explained.
“He had an option on his contract and the option was high value in terms of wages.
“I just couldn’t take that on. We have to free up some cash and I can't do that unless I do what I do at this moment in time.”