The antonyms for the phrase "utmost degrees" might include terms like "minimal levels," "moderate amounts," or "average measures." These terms all suggest a lack of intensity, extremity, or excess, in contrast to the concept of reaching the utmost or highest degree of something. Antonyms might also include the ideas of restraint, moderation, or limitation, which are the opposite of the sense of boundless or limitless potential that the words "utmost degrees" might evoke. Depending on the context in which the phrase is used, antonyms could vary widely, but they generally will indicate a lesser degree of intensity, quantity, or magnitude than "utmost degrees.