The words depreciate and deprecate are from different Latin originals, but the difference in meaning between them is being eroded in popular usage.
Depreciate is from Latin depretiare, a combination de (from) and pretium (price). “To depreciate” is to become less in value. Example: “It’s often said that a car depreciates as it is driven off the dealer’s lot.”
Depreciate is used transitively with the meaning, “to lower the value of.” Example: “The latest crisis depreciated the currency.”
Figuratively, depreciate means, “to belittle or disparage.” For example, “No matter what I do, he depreciates my efforts.”
Deprecate is from Latin deprecari, a combination of de (from, away) and precari (to pray). “To deprecate” something was to “pray it away.” The word entered English in the 17th century with the meaning, “to pray against evil, to pray for deliverance from.” For example, one might go to church to “deprecate God’s judgment,” that is, pray that it might be averted.
Deprecate has the secular meanings “to plead earnestly against” and “to express earnest disapproval of.” For example, “We deprecate the harsh action taken against the local population.”
Speakers do not always see a difference between depreciate (to belittle) and deprecate (to disapprove of). Because the distinction is a fine one, the words have become mixed up.
As a plain verb, deprecate is not as common as it was in the 19th century, but its present participle form occurs in the popular adjective self-deprecating.
As defined at the online Oxford Dictionaries site, self-deprecating means “modest about or critical of oneself, especially humorously so.” Here are two recent examples of the usage:
The iconic comedian [Joan Rivers] passed away today at 81, but she leaves behind a legacy of unrestricted humor and self-deprecating wisdom.
“Humor is an amazing quality to have,” Kunis told Glamour. “I like sarcasm, satire, self-deprecating humor.”
In researching this post, I found several depreciatory comments directed at speakers who write self-depreciating instead of self-deprecating. The sarcasm that accompanies some of these comments is misplaced.
According to the Ngram Viewer, self-depreciating predates self-deprecating by 20 years. For about 100 years, beginning in 1845 and continuing until the 1940s, self-depreciating is the more common term; then, self-deprecating soars to its modern ascendency and self-depreciating plummets.
Etymologically speaking, self-depreciating is the better choice, but self-deprecating has triumphed in standard speech; self-deprecating is the version to use if you don’t want to seem ignorant. Merriam-Webster, by the way, defines self-deprecating as “given to self-depreciation.”
Computer science has found a new use for deprecate:
deprecated (adjective): Used typically in reference to a computer language to mean a command or statement in the language that is going to be made invalid or obsolete in future versions.
Examples of deprecated in the context of computer science:
A program element annotated @Deprecated is one that programmers are discouraged from using, typically because it is dangerous, or because a better alternative exists. Compilers warn when a deprecated program element is used or overridden in non-deprecated code.
Apple has officially deprecated Java, the cross-platform runtime environment developed by Sun and now owned by Oracle, and the company has decided not to include Adobe Flash technology on its new super-slim MacBook Air notebook computers.
Bottom line: to deprecate is “to disapprove,” but in “self-deprecating,” it means, “to belittle.” In the world of computing, deprecated means “phased out” or “soon to be phased out.” Depreciate is for talking about loss of monetary value.