1. express disapproval of; protest against
1. When he disinherited his son, many relatives came to deprecate such a harsh deed and beg him to change his mind.
2. He has a tendency to deprecate his own talents and achievements.
de (away)#precari (to pray, ask, beg, request) (Latin)
censure, decry, denounce, deplore, deprecate, impugn, lambaste, reproach, upbraid
extol, laud, lionize
You can think of it as the opposite of appreciate (as in devalue against value). So lack of appreciation;ie, humiliation or belittling.