There are different ways of combining quotation and punctuation marks. In the American style, you almost always put periods and commas inside the quotation marks:

Dr Johnson kicked a large rock and said, as his foot rebounded, "I refute it thus."^[1]

It is only an accident of evolution, as it were, that the senses we are born with are not adapted to feel such things "directly."^[2]

In the British style, however, you put periods and commas outside the quotation marks, unless they are part of a complete sentence that is fully contained between the quotation marks:

Dr Johnson kicked a large rock and said, as his foot rebounded, "I refute it thus."^[3]

It is only an accident of evolution, as it were, that the senses we are born with are not adapted to feel such things "directly".^[4]

When faced with this contrast, the proper reaction is to recoil in horror at the first approach, and to look approvingly on the second. In the sentence beginning with It is only ..., the quotation is a part of the sentence, and the sentence contains the quoted word.

It is only an accident of evolution ... "directly".
[--------------------sentence---------------------]
                                        [--quote-]

Since a period marks the end of a sentence, it should not be placed before marking the end of the quotation. You can compare this with nested or hierarchical structures, or with stacks, or even with last in, first out methods of computing, inventory accounting or redundancy management. Under any comparison, the British style will seem preferable to the American. You resolve the nested item first, before resolving the parent. I do not know but suspect that this is why the British style is also called logical quotation.

In the sentence beginning with Dr Johnson ..., we do place the period within the quotation marks, because what is being quoted is a full sentence. We are placing the period to mark the end of the inner, quoted sentence.^[5]

Dr Johnson kicked a large rock ... "I refute it thus."
[----------------------sentence----------------------]
                                   [------quote------]
                                    [----sentence---]

There is no reason that there should be two different approaches to punctuation in the English language. The British approach makes more sense, so use that one.