Billy Mckay was the match-winner as Caley secured their first ever league win at Celtic Park, and Lennon was involved in a fiery altercation with a fan in the aftermath.
He said afterwards: "They are frustrated. I disagreed with them, I didn't like what they said about the team. Look, if they are not happy with what I am doing and they want me to go, I will.
"If the fans make it clear that they are not happy and they want me out then that's okay, I will do the honourable thing.
"I can't repeat it (what fans said) because it is public arena but there were a lot of expletives and heavy criticism, which I didn't think was justified and (there was) a lack of patience with the team as well.
"If there was a lack of application and commitment I would be the first to criticise the team. I didn't see that but I did see a lack of composure and quality in the final third and that's what cost us.
"If I think it is justified then I don't have a problem with it but I don't think it was justified today. But they pay their money, they are allowed to say what they like. I've got my opinions on it and sometimes I give them as well.
"I am not happy with the league form, it is my team at the end of the day so I take the responsibility for it. It's not for the lack of trying to find the answers."
Just over two weeks ago, Lennon was the toast of the town having guided the Bhoys to an historic 2-1 Champions League victory over Barcelona.