Use 'insensible' to describe someone who's emotionally disconnected from a situation or unaware of others' feelings. Despite the team's loss, he remained completely insensible.
Pro Tip 2/3
Lack of Response
'Insensible' suggests zero response to something that typically provokes a reaction. She was insensible to the audience's cheers.
Pro Tip 3/3
Hidden Intensity
Sometimes 'insensible' implies a situation's impact is so strong, it numbs people's usual reactions. He was insensible to her charms, unlike the other men.