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 Clydesdale Bank Premier League 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 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 that Celtic is always a positive club for all.
"We all know it has been a very difficult season for Celtic and we all know what has gone on. However, we must ensure that 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.
"As we move towards next season it is vitally important that we ensure we do so positively.
"However small the minority of people involved, this behaviour has no place at Celtic and I am sure as we move towards a new season and new beginning, everyone associated with the club will recognise this."
Lennon, whose team face Motherwell in the Scottish Cup final on Saturday, added: "We move to next season with confidence, we will try again to bring fast, attacking, entertaining and positive football - and ultimately, football that brings you the supporters the success which your backing deserves."