In most states you would be able to place a claim against the at-fault party's insurance policy for the damage your vehicle sustained even though you were uninsured at the time of the accident.

Normally you can contact the at-fault party's insurance company and place a claim against their property damage liability coverages for your damages. If you were ticketed for driving without insurance then you will need to take care of that citation and any penalties associated with it. Penalties can vary depending on state laws but can include fines, license suspension and/or registration suspension.

Now there may be some states that do not allow you to place a claim due to your car being uninsured at the time of the incident. For example Louisiana's Insurance Commissioner mentions this state's“No Pay, No Play” provision. What this means is that drivers who do not have the Louisiana mandatory $10,000 liability insurance forfeit their right to use the court system to sue for the first $10,000 of certain types of damages.

Thus the Louisiana Insurance Automobile Law is controlled by the "No Pay, No Play" statute, which bars motor vehicle owners who do not have liability insurance from collecting the first ten-thousand dollars of any bodily injury or property damage resulting from an automobile accident. This provision does not apply to passengers in the motor vehicle. In addition, accidents caused by drunk drivers or hit and run drivers are considered exceptions to the mandatory "No Pay, No Play" law and will allow victims to recover despite not having any insurance.

So it will depend upon your state's laws if you are able to collect for your damages from the at-fault party. Check with the other party's insurance carrier to see if you can make a claim for your damages and/or your state's insurance regulator to see what state laws allow for you to do in your situation.