The phrase "be on alert" suggests a state of heightened awareness, vigilance, or preparedness. Its antonyms could convey a sense of relaxation, carelessness, or inattention. Some possible antonyms for "be on alert" include being off-guard, unprepared, unaware, complacent, or indifferent. However, these antonyms could also imply different degrees of risk or danger. For instance, being off-guard may happen in a safe or familiar environment, while being unprepared may apply to a new or unexpected situation. Thus, understanding the context and potential consequences of not being on alert can help identify appropriate antonyms for this term.