Only one letter separates these two words, but there’s considerable difference in meaning. The word deprecate means to express disapproval of something. A synonym for deprecate in this context is to deplore.
Example: He deprecated his sister’s actions.
This means that he did not approve of his sister’s actions.
The word depreciate means to belittle or play down.
Example: He depreciated his sister’s achievements.
This means that he behaved as if his sister’s achievements were insignificant.
Depreciate also means to decrease in value. If you’ve ever owned a car, then you’ll know that every year it is worth less than the previous year. In other words, it has depreciated. The noun is depreciation, which is very common business and financial term.
Quotations from the press:
For most used-car buyers it would be a dream come true: Your car actually gains in value, instead of depreciating.
When Kelley Blue Book looked at depreciation of used cars from May 24 to the same day last year, it found 23 examples of used cars that had gained in value during that time. (USA Today)
It is easy enough to deprecate Mahler’s Third. It is inordinately long–close to two hours. It repeats ideas endlessly; much of the music could easily be exchanged with that of other Mahler symphonies; the idiom is pure Mahler with little variation from previous compositions; long stretches are unrelievedly banal. – LA Times