Horses are amazing animals but they are animals at the end and the can get scared of things that we don't even see, they can hear something that we can not hear, they can stop on the fences, they can run away, they can flip, they can have a bad distance to a fence... The list can be longer and there can be many reason for a rider to fall from his horse.
Most of the riders can blame themselves or they can blame the horse, they may think falling is for beginners but at the end of the day falling is a part of our sport. Many riders are very lucky because they do not experience a serious fall but on the other hand some are not so lucky including myself that we need to rebuilt our confidence because we experienced strong falls.
It happened to me 2 times in 20 years of riding. One was at a competition that my mare couldn't find the good distance and I wasn't good enough to help her so she fell into the fence and we rolled together on the ground. I broke my saddle as well as my nose. That made me scared of oxers for a while. For a long time and on the big fences still sometimes I am very careful with oxers. But I made myself understand that at some point if I want to keep riding and keep being a competitor, I have to face with my fears. So I started jumping many many oxers for a while until I lost that fear. Fear is a very useful emotion, it can make you miserable or it can push you forward. And it is a very natural feeling, everybody who sense the danger feels it and it is not only for humans but for animals also. So do not blame yourself because you are scared of something as long as you have a reason.
There are many reactions to fear because we are all different and we have different understanding, reactions, mentality etc. Whatever your reaction, the first thing you should do is to analyse what happened. Accidents occur for many different reasons and how you proceed to deal with it will in large part depend on this factor. You can not run away from fear but you can overcome it. It is all our in mind, the more we calm down our minds the more our body is going to react more calmer. In time we will find the balance between the mind and fear.