Like in "I am the king of the world" you can't say "I am king of world"? In these cases you need the articel?
But " a glass of water" doesn't need the article, right? As you would never say "a glass of the water" unless it is some specific water and you have a choice.
Secretary directly translates to γραμματέας and minister directly translates to υπουργός. Those are official titles, though. Some countries may refer to what we call υπουργοί in Greece as secretaries and some others as minsters.