没 and 不 are fundamentally different.
没 means "didn't"
不 means "won't" or "don't"
Actually your two sentences are perfectly normal Chinese sentences:
我没喝 means I didn't drink (it) -or- I haven't drank
我不喝 means I don't want to drink -or- I won't drink
A Chinese English Dictionary
没
ADVERB INFORMAL have not or did not
他来没来?——还没来呢。
Tā lái méi lái? —— hái méi lái ne.
Has he come yet?--Not yet.
不
1 (used before verbs, adjectives, and other adverbs; never before 有) not; won't; not want to
我不去。
Wǒ bù qù.
I'm not going. or I won't go.
他昨天不来,可是今天来了。
Tā zuótiān bù lái, kěshì jīntiān lái le.
He didn't want to come yesterday,but he came today.
So the deal is: do you want to say haven't (yet), didn't (yet) = 没 -or- won't, don't (want to) = 不. Pretty much any verb can follow 没 and 不 everything just depends on what you want to express.
有 might be the only exception I can think of at the moment but that's been covered here: http://chinese.stackexchange.com/questions/247/why-is-有-yǒu-the-only-verb-that-requires-没-while-other-verbs-can-use-不https://chinese.stackexchange.com/questions/247/why-is-有-yǒu-the-only-verb-that-requires-没-while-other-verbs-can-use-不