The appearance of quotation marks does not automatically call for a comma. If the quoted words are being incorporated into the grammar of your own sentence, punctuate the same way you would if the words weren't in quotation marks.
However, if you begin with "He says" or something equivalent and follow that with a sentence, that is a different situation and does indeed require a comma. For example:
The CEO said, "My successor is a profoundly ethical leader."