The period ends the sentence - the quote was a phrase extracted from a sentence. The end of the sentence was not within the quote - hence, the period outside the quote. If the quote was the end of a sentence, the period would stay inside the quote, and no further period is required. A sentence could actually be quoted in the middle of another sentence - in that case, the complete-sentence quotation would contain a period and another period at the end of the larger, containing sentence.
At least, that’s how I was taught.