Antonyms for "being sensible of" can include being unaware, oblivious, or ignorant. These words imply a lack of perception or understanding, whereas being sensible of suggests a heightened awareness or consciousness. Other possible antonyms may include being indifferent, negligent, or apathetic, which indicate a lack of concern or attention towards something. Overall, the antonyms for being sensible of highlight the importance of having an acute awareness and appreciation for our surroundings and experiences. By being mindful and attuned to our surroundings, we can enhance our overall well-being and lead a more fulfilling life.