Recently I came to know that there is a construction "many a man" which is equivalent to "many men". But I also noticed that the former construction is considered as singular, e.g.
Many a man has lost his life at sea.
But for the later construction we go something like this,
Many men have lost their lives at sea.
I am quite confused in the former construction. It behaves like we are talking of a single man but we are actually talking of many men. Please explain in detail why it is so.