"Operations" systems involve things like command and control, shuttle launch and recovery, tractor beams, cloaking devices, and the like.
For me, the loss of the ship's operations systems would mean that the bridge can't control anything anymore (although engines would still function, manevering thrusters would still operate, etc.), comms are down, the cloaking device is inoperative, shuttles can't launch or land, etc. Yes, the ship is effectively crippled.
Of course, you'll probably want to check that against what the NG says about it.
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz