"You either relish it or fear it," said the Hoops boss, who revealed left-back Jonny Hayes sustained a shoulder injury which requires a scan.

"So relish it. It's great. Maybe it's something new for some of the players but I think they are taking on the challenge well and I think the fans are enjoying it as well.

"There will be anxious moments as we go along. There will be a dip but, at the minute, we are in a very strong position and playing brilliantly.

"We know there can be a below-par performance around the corner but we are prepared for that as well. Psychologically that is a good win for us.

"You get 24 hours to enjoy it and see what the (Rangers) result brings and you move on to the next one.

"We were very powerful. Not only our fitness levels and the way we battled for second balls today, but the football was superb and it was a very comprehensive win against a tough team to beat at times."

Lennon waxed lyrical about Jeremie Frimpong who was named man-of-the-match. The 18-year-old right-back was signed from Manchester City at the start of the season and he has impressed the Northern Irishman.

"He is amazing," said Lennon. "That performance in isolation was one of the best I've seen from a right-back at Celtic.

"It had everything. Pace, power, assists, shots on goal, recovery runs, and he defended well.

"For a kid at 18 to come into an environment like this is daunting but he is handling it brilliantly. He has made us better, no question."

Lennon also welcomed back striker Leigh Griffiths, who came off the bench in the second half to great cheers to make his first appearance since the end of August due to personal problems and injury.

Lennon said: "You can see how popular he is with the fans. You see he still has a bit to do but his work-rate was good.

"It is a timely comeback with the volume of games coming up so we just want him to get fitter and stay at that level. There is plenty more to come from him."

Livi boss Gary Holt, whose only win in 11 matches has been the victory over Celtic last month, thought his side were "well in the game".

He said: "I know everyone will pick up the papers and look at it as 4-0, but I just thought individual mistakes at times in the game cost us.

"For effort and commitment and all the things you look for, team shape, being brave at times in possession, I thought we had that.

"At times I felt we could've been braver but, if you take the goals out of the game, they didn't cut us open too many times."