Lambert, who won the Champions League as a player with Borussia Dortmund before moving to Parkhead, says he enjoyed his eight years in Glasgow but has moved on.
He was sacked as Ipswich Town manager after a fall-out at Portman Road last week. He is set to be replaced by Paul Cook at the skybet League One club. However he is not quite as keen on a quick move back into management despite the vacancy in the east end of Glasgow.
He said: “I had eight great years there and success there. I wouldn’t want to ruin that relationship I have with the Celtic supporters. Glasgow was my life a long time ago, I’ve moved on.”
Speaking on the GO Football Show, the Scotland international also weighed in on Lennon’s departure last week and criticised the players’ performance at Ross County in what transpired to be the manager's last match.
Lambert said: “I watched the game against Ross County the other week and they never turned up. They never laid a glove on them. That's not Celtic. Some of them looked as if they didn't want to be there.”
He added: “Looking at the Ross County game I think they let Lenny down. They've got to look at themselves in the mirror and say, 'we didn't perform'.
"It's dead easy to hide behind a manager when things are not going right and they've got to take responsibility themselves."