The League Cup defeat prompted angry demonstrations from fans calling for Lennon to go, with chief executive Peter Lawwell urging unity on Tuesday.

"On the scenes on Sunday, we're hurt and disappointed," Lennon said.

"I understand the frustrations of the supporters because we are not in a great run at the minute. But it serves no purpose, particularly for the players.

"I'm old enough and big enough to take criticism and abuse. Some of it is justified and some of it is over the top. That is the role of a manager and that is the responsibility you have to bear.

"They [the players] felt the wrath of the supporters. It surprised some of them, it shook a few of them up. But they want to put things right for them and obviously the club and myself as well."

Lennon has held talks with Lawwell and Celtic's majority shareholder Dermot Desmond about their poor recent run, and continues to have their support.

Asked if he felt the County defeat would end his tenure, Lennon replied: "Not in my heart of hearts, but I could understand if that had been the case.

"I am very grateful. They are not a board that sack managers for the sake of it. We have had great success. We are going through a tough time but they don't leave you out on the lurch."

Celtic face Serie A leaders AC Milan on Thursday in the Europa League, but cannot progress in the competition after back-to-back 4-1 losses against Sparta Prague.

They then host St Johnstone on Sunday in the Scottish Premiership looking to remain on the coat tails of leaders Rangers, who are 11 points clear having played two games more.

Lennon admitted "it sounds like I am repeating myself time and time again", but reiterated his belief that his side's form will improve as they bid to win a record 10th straight league title.

"For 20 years, I have done everything in my power to bring success to the club and the fans," the Northern Irishman said.

"That is not going to change on the run of a bad month or people being upset by my style of management.

"It only takes a flick of the switch. I think we are lacking a little bit of confidence, a little bit of belief. But it can turn around very quickly and then it is baby-steps after that, build, build, build, build."