Ottoman leaders publicly conceded European naval superiority by the mid-1500s.

Evidence

A few years later, Lutfi Pasha, the Grand Vizier of Suleyman the Magnificent, raised the matter again with his sovereign, and told him: “Of the previous Sultans, there were many who ruled the land, but few who ruled the sea. In the conduct of war at sea, the infidels are superior to us. We must overcome them.” — Bernard Lewis, From Babel to Dragomans, 678