UEFA has opened disciplinary proceedings into the matter and Lawwell has slammed those responsible for the banner in an impassioned message on the club's official website.
"Last night was nothing more than clear disrespect for the club and our supporters who now face another UEFA charge," the statement read.
"There have now been a number of UEFA charges made against the club during the last three years, relating to behaviour, displays and pyrotechnics - it cannot go on any further.
"Let's be very clear. Following the actions of a small minority, these charges are made against the CLUB. It is the reputation of Celtic, our great club and our great fans which is damaged, while others carry on indulging in such behaviour.
"Regardless of the political views people hold, football stadia, whether it is Celtic Park or anywhere else, should not be used to promote these.
"This is something which all football authorities, including UEFA, have stressed for some time and something well known by all supporters.
"The club don't want it, our manager and our team don't want it, our supporters don't want it and the football authorities don't want it - it has to stop.
"Celtic is a world-class football club and rightly proud of its wonderful reputation in the game. This is a reputation hard-earned by our supporters over many years. We cannot and will not allow this reputation to be tarnished any further."
Celtic were fined £4,221 earlier this season by UEFA after fireworks were set off by supporters during their Champions League qualifier against Northern Irish side Cliftonville.
They were also punished twice during their 2011/12 season Europa League campaign after supporters displayed an offensive banner and set off flares during an away game with Udinese.
Celtic were also handed a £13,000 fine for "illicit chanting" in the same competition during their game with French side Rennes.
Neil Lennon's side cannot now qualify for the knockout stages of the competition or the Europa League after they were beaten 3-0 at Parkhead but they now face problems off the pitch, with UEFA due to consider the matter next month.
"Disciplinary proceedings have been opened against Celtic FC for an incident of a non-sporting nature (illicit banner) at last night's UEFA Champions League match against AC Milan in Glasgow," read a UEFA statement.
"The case will be dealt with by the UEFA Control and Disciplinary Body meeting on 11 December."
The disciplinary code of European football's governing body states clubs may be subject to disciplinary measures if supporters are found to have used "gestures, words, objects or any other means to transmit any message that is not fit for a sports event, particularly messages that are of a political, ideological, religious, offensive or provocative nature."
Meanwhile, a man has been reported to police for allegedly shining a light onto the pitch at Celtic Park.
"A 25-year-old man is subject of a report to the procurator fiscal in connection with allegedly shining a laser pen on to the pitch at Celtic Park during the match on Tuesday 26th November," Police Scotland confirmed.