The Cumbrians must beat Wolverhampton Wanderers on Saturday to have any survival hopes, although if Crewe Alexandra draw or Tranmere Rovers win, they are down.
"There is deep sadness because we look like we'll lose League One status. Planning starts tomorrow and I'll leave no stone unturned to try and get us back there," Kavanagh told BBC Radio Cumbria.
Kavanagh's side won three matches consecutively when the 40-year-old took over, but have failed to claim back-to-back wins since.
Carlisle are currently in the relegation zone, three points adrift from safety as they head into the final match of the season on Saturday.