My native language is Portuguese, but I'm an English Teacher an I'm using Duolingo to improve my German. In Portuguese, we have an expression very common that is: "Não, eu não.", which means "No, I not" literally translating [not used in English], or "Não, não eu", translating "No, not me". This expression doesn't use a verb in Portuguese. The same thing happens in German. "Nein, Ich nicht." Since there is no use of a verb, the translation in English couldn't be "No, I don't" or "No, I'm not", because these expressions use a verb. The only expression with similar meaning that could be used in any case would be "No, not me."