The quotation Robert F. Kennedy used in his remarks on the death of Martin Luther King, Jr. comes from the play Agamemnon by the Greek tragedian Aeschylus (525-426 BCE).
The quotation as given by Robert F. Kennedy,
In our sleep, pain which cannot forget falls drop by drop upon the heart until, in our own despair, against our will, comes wisdom through the awful grace of God.
is derived from Edith Hamilton's classic study, The Greek Way . The passage has been rendered in different ways by differnet translators.
The saying that Robert Kennedy attributes to "the Greeks" at the end of his speech -- "to tame the savageness of man and make gentle the life of this world" -- has also been credited to Aeschylus but has not been found in any of his extant works.
The entire text of Robert F. Kennedy's remarks is available here on the Kennedy Library's Website.