@nebulos both are correct with subtle differences in favoured reading. “he said morosely” reads as though “morosely” is a quality of the speech itself; his words were morose words, they had a morose inflection. “he said, morosely” is less making a statement about the words and more making one about him: he was morose when he spoke. (the “-ly” is superfluous in this case; “he said, morose” works just as well; but again there are subtle differences which might lead you to the “-ly” form.)

the above notwithstanding, in practice, it’s probably more important to go with the version that flows better in the context that it is being used than worry about such subtleties of meaning