I think that this line comes from Aeschylus' Agamemnon, which was first staged in 458 BCE. I believe this line is spoken by Cassandra, who is a female Trojan war captive whom Agamemnon has brought back with him from the war.
After Agamemnon returns and is led into the house by his wife Clytemnestra, Cassandra remains outside and begins to make a number of prophetic comments to the elders of Argos about what has happened in this house and what will happen to Agamemnon himself (i.e., that Clytemnestra and Aegisthus are going to kill him). Cassandra also predicts her own death to the Argive elders.
In the course of her prophetic frenzy, Cassandra cries out to Apollo, who is a god of, among other things, prophecy. It was Apollo who gave Cassandra the prophetic gift that she possessed. Unfortunately for Cassandra, Apollo also caused the Trojans not to believe Cassandra's prophecies. Thus, Cassandra regards Apollo as her destroyer and his causing of her prophecies not to be believed may be the source of this destruction.