Antonyms for the phrase "to great degree" would include phrases such as "to a small extent," "minimally," or "not at all." These phrases convey the opposite meaning of "great degree" by suggesting a lack of intensity, seriousness, or impact. Other antonyms might include words like "modestly," "reasonably," or "marginally." Additionally, words like "inadequately," "insufficiently," or "disappointingly" could be considered antonyms, as they suggest that the level of whatever is being described falls short of expectations or needs. Ultimately, the antonyms of "to great degree" will depend on the context in which it is used and the specific connotations that are intended.