Decry, depreciate, disparage, derogate, detract, belittle, minimize mean to write, speak, or otherwise indicate one’s feeling in regard to something in such a way as to reveal one’s low opinion of it.
Decry implies open or public condemnation or censure with the intent to discredit or run down someone or something.
Depreciate implies a representation of a person or thing as of smaller worth than that usually ascribed to it.
Disparage implies depreciation by more subtle or indirect methods (as slighting, invidious reference, or faint praise).
Derogate and detract (both with from) stress the idea of taking away, positively and injuriously, especially from reputation or merit; derogate from may be used with an impersonal subject only, detract from with either a personal or an impersonal subject.
Belittle and minimize both imply depreciation, but belittle suggests an effort to make a thing contemptibly small, and minimize to reduce it to a minimum or to make it seem either disparagingly or defensively as small as possible.