Very sorry about your bad experience.
It is good to see that you respect the animals. You have my respect in that regard. (IN MY OPINION) I believe the people who dont respect the animals are the ones who would prefer someone else kills them. Think of the alternative. Would you rather the animal be alone and killed by a machine?
It might sound a little crazy but, I always say a small prayer afterwards. It seems to help me come to terms with it all, and puts things in perspective. Take it as a good time to reflect about life and death. Its not good to ignore it and hold it all inside. If you need to cry, go ahead and cry. The animal never goes to waste entirely. Whether its feeding the plants or feeding you, that is just the circle of life.
One thing I have learned when killing animals for food is be quick and decisive. When you are nervous about it or squimish it usually results in prolonged suffering of the animal. Your skill at doing it determines how humane it is, not exactly the tool. I personally prefer to do it the axe and stump way. However, I have been in survival situations where I have killed animals with my hands, which at times can be much more humane and quicker than a knife.
And to the person who said, "being a vegetarian is more healthy". Thats not entirely true...Everything in moderation my friend, balance is the key.