I'm guessing that this case may have been brought in small claims court. If so, the appeals process may be different. There are usually forms made available to you and information stated on the judgment you received. There is a limited amount of time to appeal (perhaps as little as 30 days) and virtually every appeal requires you to convince the reviewing judge of the following: a clear material error in law or fact was made so that if the case was tried and the proper law or facts used, the outcome would be very different. For example, if the judge used the wrong law to determine the amount or wrote down the wrong amount. In addition, an "arbitrary or capricious decision" of a judge might be appealed - that the ruling appears to clearly disregard law or logic and represents some type of unfair advantage provided to the non-appealing party. I'm simplifying this for you - in short, you need to show a judge that it's very easy to see a substantial mistake that would make having another case the only fair solution. You bear the burden of convincing the court of the appeal.
In this instance, I'm guessing that you think that the damage is less than the value of the car. But if the car is totaled and the cost of fixing the damage is greater than the value of the car, the ceiling of recovery would be -- the total amount of the car. For example, you damage a bumper which costs $1,500. But the replacement cost is $3,000 because the number of hours to remove and replace it and to fix minor damage around it is $2,000. If so, the amount of recovery is capped. Now if the value of the car wasn't proven, e.g. the bluebook value was $1,000 and the judge just took the word of the plaintiff without so much as an estimate or bluebook value that the value of the car was $3,000. Good luck.