Then Samuel took the horn of oil, and anointed him in the midst of his brothers: and the Spirit of Yahweh came mightily on David from that day forward. So Samuel rose up, and went to Ramah.
Actually, David had a great admiration for Saul. Of course just a young boy, and he was at that hero age, and Saul, big, tall, handsome fellow became sort of a hero in David's eyes. David always respected Saul right to his death and even after his death. David never lost his respect for this man.