The AP Stylebook, The Chicago Manual of Style, and the Merriam-Webster Guide to Punctuation suggest that commas around a quote or fragmentary quote depend on the quote’s function within a sentence and that a comma need not always set off a quote.
I would love to do as you say and “go my own way.”
The president replied that the gesture was “gracious,” and that she looked forward to “cherish[ing] this memory in the future.”
“Turn the other cheek” was a phrase he used often and loudly.