The Northern Irishman was involved in an altercation with two of his own supporters behind the dug-out late on in his side's 1-0 defeat to Inverness Caledonian Thistle yesterday, and said he was prepared to end his 12-year involvement at the club if that was what the fans wanted.
Although Celtic have dropped 17 SPL points already this season, the club still top the table with a game in hand and stand one match away from booking their place in the Champions League last 16.
"If fans make it clear that they are not happy and they want me out then it is OK, I will do the honourable thing," said Lennon.
"I understand that they [the fans in question] were frustrated, but I disagreed with them. I didn't like what they were saying about the team. If they want me to go then I will. I can't repeat what they said, but there were a lot of expletives in there and heavy criticism, which I didn't think was justified. If there was a lack of application and commitment I would be the first one criticising, but I didn't see that today.
"They pay their money and they are allowed to say anything they like. Sometimes I say my opinions as well. We are in four competitions, but I am not happy with the league form and it is my team so I will take responsibility for it. It is not for the want of trying to find the answers."