The Mekhilta DeRabbi Yishmael draws a pointed contrast between two moments of song in Israelite history, and the difference reveals something fundamental about the nature of the Song at the Sea.
When the Torah records "Then Moses and the children of Israel sang this song to the L-rd" (Exodus 15:1), the Mekhilta emphasizes those last two words: "to the L-rd." The Israelites directed their song exclusively to God, not to any human hero, not to Moses the leader, not to any warrior or general. The praise went upward, to the One who had actually split the sea and drowned the Egyptian army.
The Mekhilta then contrasts this with a very different scene from (I Samuel 18:6): "And all the rejoicing women went out." That verse describes the women of Israel singing and dancing to celebrate David's military victory over Goliath and the Philistines. Their song was directed at a human being, at flesh and blood. "Saul has slain his thousands, and David his ten thousands," they sang, and their praise of a mortal man led directly to jealousy, conflict, and years of bloodshed between Saul and David.
The Mekhilta's point is sharp: at the Sea, Israel got it right. They sang to God and not to flesh and blood. They recognized that the victory belonged entirely to the Holy One, Blessed be He. No human hand split the waters. No general devised the strategy. God alone acted, and Israel alone witnessed, and the song they sang acknowledged that truth without dilution. The Song at the Sea became the model for how praise should be directed, always upward, always to the Source of deliverance, never to the human instruments through whom deliverance might come.