Boss Keith Curle has let Asamoah, Troy Archibald-Henville, Angelo Balanta, Arron Bradbury and Dan Hanford leave the League Two Cumbrians.
Bastien Hery, Louis Pedro, Steven Rigg, Antony Sweeney and Joe Thompson have also been released.
Defenders Alexander McQueen and Tom Miller have verbally confirmed to Curle they will sign new deals.
Dave Atkinson, Patrick Brough, Mark Ellis, Mark Gillespie, Danny Grainger, Jabo Ibehre, Luke Joyce, Jason Kennedy, Michael Raynes and Charlie Wyke are all contracted for next season.
Carlisle United have confirmed that 10 players will be released, including striker Derek Asamoah.