Khan was trying to run a ship usually crewed by at least 300 with a crew of about 60. Even Enterprise with a full (admittedly mostly cadets/trainees) crew faced huge damage-control issues.
Where are those numbers from? not that it matters much, the next movie canonized that a chimpanzee and two trainees can run a starship.
Not only that, the commander of an enemy ship with about twelve men thought they could board and overtake it.
Enterprise must be a sleeper ship.