With the home side trying to claw back Billy McKay's 65th-minute strike late in the game, the former Celtic skipper remonstrated with angry supporters behind his technical area and the match ended with a crescendo of boos from many of the frustrated Hoops support.
"They are frustrated. I disagreed with them, I didn't like what they said about the team," Lennon said. "Look, if they are not happy with what I am doing and they want me to go, I will."
The Parkhead side have taken only one point from the last nine at home but remain top of the league by a point and are within one game of reaching the last-16 of the Champions League due, in part, to an incredible 2-1 home win over Barcelona earlier in the month.
However, in the post-match press conference the former Celtic skipper was clearly enraged by some of the criticism.
"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," he added.
"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."
The visitors bounced back in some style from their 5-1 home defeat to Motherwell last week. It was Caley's first league win at Parkhead - which Terry Butcher described as "mind blowing" - to add to the Scottish Communities League Cup win over Rangers at Ibrox last month.
The former Well boss said: "To win as a manager for the first time and to beat both Glasgow clubs in the same season on their own patches and keep clean sheets, is fantastic.
"We have created history all the time and we intend to keep on doing that. We got rid of last week very quickly, they are a great bunch of lads."
Source: PA
Source: PA