Why would you?
The car is in an accident. It is a GIVEN that the value of the car has gone down.
It'd be like getting a broken bone, and claiming the broken bone, then asking if you can claim injury on top.
Your insurance claim is to reimburse you for the damages to your car. Since they pay to repair the damages, it brings your vehicle back to it's original value. Or close to it. So, there's no depreciation.
Unless the car was totaled, but then it's a salvage vehicle, and that's a different story altogether.