No, if you were at fault then you could not place a claim with the other party's insurance and have it accepted. The other party would have to be found liable or responsible in some way for their insurance company to accept a claim for your vehicle's damages. If you are clearly at fault and take blame for the accident then you have no basis in which to file a claim against the other driver’s insurance policy.

As you have already found out from your insurance agent with only comprehensive coverage, also known as "other than collision," your damages from an accident is not covered. Comprehensive coverage covers damage to your car if it is stolen; or damaged by flood, fire, or animals.

With collision coverage one is covered for damages to their car hits, or is hit by, another vehicle, or other object. Collision pays to fix your vehicle less the deductible you choose. If you were at fault and without collision insurance on your vehicle then you will be left to pay personally out of your own pocket for the needed repairs your vehicle now needs.