Here is a quick rundown of their definitions:
Depreciate is used to denote objects whose values have dropped in price over a period of time after you have bought them. This is often applied to houses, cars, computers, etc.
Deprecate is a term for items that should no longer be in use. Common uses are in computer software versions, in which an older version is said to be no longer supported. A related term is self-deprecating humor, which is the term for comedians who make jokes about themselves.
Notice the similarity in spelling between the two words. The latter is missing an i and has one less syllable. Most English speakers haven't encountered deprecate that much, it is usually seen in written form rather than spoken. This is probably the cause of the confusion over the words, and that is why depreciate is often used in place of either of those words.
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