Compare:
“Did you call your mother on her birthday?” my wife asked yesterday. I shook my head and muttered “Nope.”
with:
More informal versions of the negative answer “no” are “nah”, “nuh uh”, and “nope”.
First sentence: reported speech.
Second sentence: not reported speech. The period clearly belongs outside the quotation marks here.
Do please try to avoid the one-word bon mots in the future, dear chap; they’re best fit for gay cocktail parties on the lawn and convivial evenings at the supper club rather than discussions of grammar and punctuation. And then only if you’re Oscar Wilde.