Celtic chief executive Peter Lawwell apologised to Dundee and promised strong action after a number of supporters were ejected from Dens Park during the encounter, which Celtic won 2-0.
Lennon said: “We have a fantastic reputation wherever we go and we are very proud of that and we want to preserve it. Don’t tarnish the reputation of the club please.
Dundee operations manager Jim Thomson said there was “serious disorder” in the stadium concourse and “widespread” drunkenness.
Police reported five supporters, including four away fans, to the procurator fiscal, while the home club said many more were ejected.
Thomson said: “I have never seen anything like the behaviour of the Celtic fans in the 20 years I have been running games at Dens Park.