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.
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.
Lennon said: "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 a 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 today 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."
Lennon claims his side need to sharpen up in front of goal.
"I was very disappointed. Our play in the final third wasn't good enough," he said.
"If you can't keep clean sheets and keep missing easy chances you are liable to be beaten.
"With the amount of possession we had, the wastefulness has to be rectified very quickly.
"I didn't think we deserved to lose the game but the home form is becoming a concern, it is one point out of nine and that is simply not good enough."
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 Rangers and England player 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."
McKay said: "It was great for me to get the winner. Barca came here and they are probably the best team in the world and didn't get a result but we stuck to our task and got the win.
"I hit the bar and then it got cleared off the line after that.
"We have lost a few late goals so it was great to hang on and grind it out. We had a plan to frustrate them, keep our shape and it worked."