No, it shouldn't be accepted. "i don't want it anymore" would be: "Non lo/la voglio più" The pronoun "ne" has a meaning "of something", just think of this conversation:

English:

• Do you want some of these apples?

• No, thanks, I don't want any of it.

Italian:

• Vuoi di queste mele?

• No, grazie, non ne voglio.

What you want to say would look different. Look at this conversation:

English:

• Do you still want this apple?

• No, thanks, I don't want it anymore.

Italian:

• Vuoi ancora questa mela?

• No, grazie, non la voglio più.

So, remember: "ne" can only replace structures with "di+anything". And it can stand in idiomatic phrases like "andarsene", for example, which means "to leave", and is conjugated like this:

(io) me ne vado

(tu) te ne vai

(lui/lei) se ne va

(noi) ce ne andiamo

(voi) ve ne andate

(loro) se ne vanno

Yes please! I wrote this too

"ne" is a pronoun meaning "of it", "about it", "from it", "of them", etc.

http://italian.about.com/library/fare/blfare167a.htm