In both Dutch and English, "drink" can't take a reflexive pronoun here. In this English sentence, "ourselves" is serving a different function than it serves in "We see ourselves." In "see ourselves," it is a reflexive pronoun -- it is taking the action of the verb. In "drink it ourselves" it is an emphatic pronoun -- it emphasizes the idea of "we" that is already expressed in the sentence. The sentence would make perfect sense without it. "We drink it." We just want to call attention to the fact that it is, in fact, we who drink it, and that we probably are doing it alone, to the exclusion of others.
I don't know how Dutch characterizes these distinctions, but they use different words for the two functions. "Mijzelf/jezelf/zichzelf/onszelf" are like English's reflexive pronouns. "Zelf" is used, it seems, where we would use our emphatic pronouns.
The truth, at least to me, is that English is more confusing than Dutch in this regard, since we are using the same word for two different things.
I hope that helps.