I know it's preferable not to end a sentence with words in quotation marks, unless the words in the quotation marks comprise a full sentence in and of themselves. But if you must (or prefer to) end the sentence with words in quotation marks which do not comprise a full sentence of themselves, is it correct to put the period inside the quotation marks, or outside?
You're asking about the relative order of a comma or full stop (period) and closing quotation mark.
AmE (unlike BrE) has a rule that when a comma or full stop is adjacent to a closing quotation mark the latter must follow, irrespective of the relative semantic scope. BrE tends to position the punctuation marks according to scope, i.e. the meaning. The following examples represent uniform BrE practice:
(1) He'd apparently just been trying to 'help one of my patients'.
(2) Instead of doing his homework he was watching 'Neighbours'.
(3) I replied, 'It was all Angela's fault.'
In (1) and (2), the quotations are sub-clausal and do not license any internal punctuation; the full stop thus belongs semantically in the matrix and hence is locate externally (contrary to AmE practice). In (3), by contrast, the quotation is a sentence and thus sanctions a full stop; from a semantic point of view the matrix also merits a terminal full stop, but this is suppressed, so this time BrE matches AmE practice.