After the battle, Harry thinks that Marcone is in a great position to claim the eye or the spear. Marcone doesn't. But later on after the scene on the water beetle, when he makes it to shore. He only mentions giving the Eye to Alfred for Safe keeping. I don't recall seeing any mention of the spear of destiny after he puts it away which is right after Marcone Vanishes behind a veil (establishing he is capable of subtle magic). I see four possibilities. 1) Marcone took it while veiled and used psychomancy to erase the act. 2) Justine/Nemesis took it from him in the water, and he was too zonked to realize it 3) He still has it ON HIM. (which seems a really bad Idea) 4) he gave it to Alfred but doesn't remember/didn't mention it. (Unlikely I think)