Whenever you relate to a specific quantity, you don't use the article and du/de la/des turns into de. And not having something, i.e., having zero of it, is also a specific quantity. Hence in negations you just use de.

J'ai du lait. -- I have milk. (no specific quantity, hence du)
J'ai un peu de lait. -- I have a bit of milk. (un peu is a specification of quantity, hence de).
Je n'ai pas de lait. -- I don't have milk. (no milk is also considered a quantity, hence de).

-- Chris (not a native speaker).

I would love to see Chris' answer turned into a lesson for all phrases that include only "de" and "du, de l', de la, des".