These words are related in meaning: "to speak of as unimportant," "to regard something as less important or impressive than it apparently is." Disparage is a stronger word than belittle in that it tends to bring reproach or discredit upon the topic being considered, whereas belittle means simply "to make less," "to minimize": "Don't belittle my efforts; I'm trying hard." "The prosecuting attorney disparaged the testimony of the witness."
Dictionary of problem words and expressions. Harry Shaw. 1975.