Non-preferred sounds clunky to me and words like alternative, I feel, don't convey the sense of "the set of things I really don't like".
Edit: Perhaps the context will help. In this version, I've used tchrist's suggestion of disliked:
Most parts of the brain have preferred patterns of input that those parts link to characteristic patterns of output. Many disorders arise when a brain region receives patterns of input it dislikes or cannot link the preferred input to its characteristic output.
I want to avoid too much anthropomorphism because this is for a scientific paper. The field already uses the word "preferred". In the section intended for a general audience I wanted to avoid using technical words but not accidentally convey something.