To depreciate is (1) to lessen in value, or (2) to lower the value of something, especially by falsely undervaluing, disparaging, or belittling it. The word is most common in financial contexts. Deprecate traditionally means to express disapproval of, but over the last century it has gained another sense—to disparage or belittle—that makes it roughly synonymous with depreciate in that word’s second sense.
The newer sense of deprecate is what’s meant in the common phrasal adjective self-deprecating, which means undervaluing oneself. Self-depreciating would carry roughly the same meaning, but it is likely to be considered a misspelling because self-deprecating is by far the more common form.
The most straightforward application of these words is in financial and monetary contexts, where depreciate is the appropriate word—for example:
Vehicles with high retained value in their early years, he says, usually last longer than vehicles which depreciate more quickly. [Globe and Mail]
The good news for U.S. farmers is that the dollar will continue to depreciate against most currencies over the next few years. [Southwest Farm Press]
Deprecate is occasionally used in its older sense, to express disapproval—for example:
I deprecate Bill Aitkens’ reported comments, which were rightly greeted with outrage from both general public and across the political spectrum. [quoted in New Statesman]
From this perspective, to deprecate multiculturalism is to deprecate tolerance. [Independent]
But mostly deprecate is used in the sense to disparage or belittle:
I do not mean to deprecate the importance of air and naval power, which matter greatly. [Frum Forum]
Microsoft exerted control over developers by requiring changes to boot-up screens and deprecating Netscape’s ability to compete in browsers. [The Register]
And although self-depreciating would make as much literal sense as self-deprecating, the latter appears about 40 times as often. Here are a few examples:
First, being self-deprecating always, always works. [Los Angeles Times]
Self-deprecating irony has always balanced the brimstone, and the beard that looks like a prophet’s may just be because he’s Texan. [Independent]
Gadsby’s humour is a phlegmatic mix of dry observation and self-deprecating storytelling. [Sydney Morning Herald]