You are absolutely right that there are a LOT of references in the Bible to instrumental music, especially to their use in connection with the Temple (i.e., Old Testament) worship. There are also references to instrumental worship in Heaven. Instruments were apparently not used in the synagogues. There are no Biblical references to instrumental worship in New Testament worship. This, I believe, is why we use the term "a cappela" (meaning "in the manner appropriate for the chapel") to refer to unaccompanied singing.
Think of it this way: If I order a hamburger, should the waiter bring me a cheeseburger? I don't NEED to say "Thou shalt not serve me cheese". If I had wanted cheese, I would have asked for it.
Check out Ephesians 5:19 and Colossians 3:16.