The answer you have accepted is in fact not correct. From ancient to modern times (e.g. 1 Cor 15:27 (ASV, Darby, ESV)), quotes have been set off from the main text by commas. Observe that the ESV's rendering of that verse, as well as all other quotations is, in accordance with modern English, done using not only the two commas but also the opening and closing quotation marks.
For “God has put all things in subjection under his feet.” But when it says, “all things are put in subjection,” it is plain that he is excepted who put all things in subjection under him. [See the full context at the link.]
So if you want to follow the ad-hoc customs that English writers have been following for centuries, then the reason to insert commas is not because of grammatical function at all, since the quoted example clearly has "all things are put in subjection" as the object of "says", and yet the translator inserted a comma in-between!
However, if you want to be logical and ignore the established customs in written English, then you ought to write:
For [it says] “God has put all things in subjection under his feet.”. But when it says “all things are put in subjection”, it is plain that he is excepted who put all things in subjection under him.
This logical version properly respects the status of quoted phrases as strings, so we would not be at liberty to use the full-stop in the quotation to double as the full-stop outside, nor would we insert any spurious comma at the end of the quotation since it literally does not occur in the original. (This fact is absolutely clear in the above example!) Naturally, there would also be no comma before the quotation, but that is really the least of your worries if you are trying to convince a publisher to let you use logical quotations...