"Thanks, I don't need shoes."
Translation:Gracias, yo no necesito zapatos.
Good question. The book "A New Reference Grammar of Modern Spanish" covers this topic in chapter 3 Articles on pages 27-48. Section 3.2.1 Uses and omission of the definite article is on pages 28-41.
As I can't retype all that information here (well maybe I could, but...), I highly recommend the book.
I do know that the specific/non-specific rule that we use in English often doesn't work when applied to Spanish as you've discovered.