There are really two types of problems that people commonly call target panic, and it would probably be better if they had different names, because they require different cures.
The first type is caused by the subconscious mind jumping the gun on the shot. You want a surprise release, so your body won't react to the shot until the arrow has left the bow, so you have turned the job of releasing the arrow over to the subconscious mind. This works fine for a while, until your subconscious mind starts anticipating the shot and releasing early. Since you don't have any conscious control over your subconscious mind, you can't just decide to stop releasing early. All the cures for this problem have to do with re-programing the subconscious mind to not release the arrow until you are at full draw and ready to shoot.
The second type of target panic has to do with the conscious mind. Your own mind is your worst critic, and you may find that there is a voice in your head telling you how you ought to shoot the shot. When you miss the shot anyway, the little voice starts picking your shot apart, and introduces doubt that your next shot is going to be any better. The doubt creates anxiety, and the anxiety creates tense muscles. You may feel like the connection between your mind and body has been broken, and that you have lost most of your physical awareness of what your body is doing during the shot. Rather than contracting the muscles you need, and relaxing the rest of them, you contract opposing muscles at the same time and begin to work against yourself. The solution to this problem is two step: first, through mantras or breathing, you stop the little voice, which really means that you stop all cognitive or conceptual thinking during the shot process. Cognitive and conceptual thinking is never about what is happening right now; it is about what happened in the past, or what may happen in the future. The only thing that is happening right now is what is going on in your body and what you can sense with your eyes, etc. It is only awareness OF those things (and not thoughts ABOUT those things) that can help you during your shot. After the little voice has been stopped, the next step is to regain and increase your physical awareness of what your body is doing during the shot.