Dead vs Illusion

[MunchingKing]

Last night some friends and I played a game and a situation arose where my friend was in combat with a monster he was not going to beat. He played Dead on the monster. However, I wanted to play Illusion in response. He argued that the monster was already dead so combat was over and I couldn't play Illusion. My question is: Could I have played Illusion in response to him playing Dead on a monster?

Thanks.