I have often been confused with these two words and their usage as these are very similar in spelling and meanings. Today, after a bit of googling, I found the real context of them.
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.
Eg : The pound is expected to depreciate against the dollar
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.
Eg : This feature of Subversion is deprecated.