Antonyms for "kept an eye on" could include "neglected," "ignored," "overlooked," "abandoned," or "disregarded." These words suggest a lack of attention or care for monitoring and observing something or someone. Neglecting or ignoring something can lead to negative consequences, whereas actively keeping an eye on something can prevent mishaps or problems from arising. It is important to be mindful of what we are responsible for and to take the initiative to oversee and manage it. By doing so, we can avoid potential issues and maintain a sense of control over our surroundings.