The 22-year-old midfielder joined the Blades on loan from Hearts in January with a view to a permanent move in the summer.
But despite scoring five goals in 17 appearances, Clough has opted not to sign Holt.
He told the club website: “We’d have loved to have kept Jason, but we thought he was just too similar to Stefan Scougall who we have under contract.
“We brought Jason in because Stefan had a few knocks and niggles and for him to score the amount of goals he did from midfield was excellent.
“Jason did brilliantly for us but we just need a different kind of player next season, we need more of a physical presence because when Chris Basham has played there he has done ever so well and shown what a quality player he is.”