IRA chants were heard at Tynecastle last week when some Celtic fans clashed with stewards following an incident on the touchline which saw a fan charged with assaulting Lennon.
The Northern Irish manager again praised the supporters for their "magnificent" response to him and the team on Sunday as Celtic lost out to Rangers in the SPL title race despite victory over Motherwell.
But he urged a minority of fans not to tarnish the club's reputation.
In a statement on the club's official website, Lennon said: "Celtic is rightly proud of its unique history and also of its open, inclusive and welcoming spirit. It is this which we hold dear.
"While we are delighted with the support we have received throughout the season, it is very important that we ensure Celtic is always a positive club for all.
"We know it has been a very difficult season for Celtic and we all know what has gone on. However, we must ensure we do all we can to uphold the club's reputation.
"In recent times, unfortunately, there has been a re-emergence, from a small minority, of some of the singing and chanting which is simply not acceptable around our club.
"This has no place at Celtic Park or at any of our matches and it must be tackled. All this does is tarnish the great name of Celtic and embarrasses the club."