Typically, yes. You should report this loss to the other party's insurance company. A licensed claims adjuster will obtain your version of the accident as well as the other person's version. He or she will consider all of the facts along with any other information relevant to this indecent. Ultimately, the decision will be made by the claims adjuster.
In addition, you might receive a citation from the responding law enforcement agency for not having your own insurance. This could include a monetary fine and you may have to show proof that you have obtained an insurance policy. Needless to say, this policy will not cover you for the loss that already occurred.
Also, your license might be suspended and you may have to satisfy the financial responsibility laws. What this means is that you will have to buy an 'SR22' insurance policy. The SR22 filing is proof of insurance that is filed with the Department of Motor Vehicles in your state to re-instate a driver's license that has been suspended.
If you would like to know how this might affect your insurance rates you can get a car insurance quote here.