AC Milan have described UEFA's decision to hand Celtic a small fine but ban goalkeeper Dida for two Champions League matches as a 'disproportionate and illogical' response to last week's Parkhead drama. Celtic must cough up £12,500 now, with the same sum suspended for two years, after a 27-year-old home supporter ran on to the pitch and gave Dida a cheeky tap following Scott McDonald's winning goal in the 2-1 victory over Milan on October 3. UEFA's control and disciplinary body last night found Celtic guilty of charges of 'lack of organisation' and 'improper conduct of supporters', and the financial penalty was described by Hoops chief executive Peter Lawwell as 'proportionate to the incidence in question and a fair outcome'. Celtic could have received a far greater punishment and will not appeal, however Milan have confirmed they will mount a challenge to UEFA's independent control and disciplinary body verdict. Dida's reaction to being approached by the fan was found to have breached UEFA's 'principles of loyalty, integrity and sportsmanship'. AC Milan lawyer Leandro Cantamessa said: 'The impact of the sentence is disproportionate and illogical. 'I have no issue with Celtic but I am only trying to establish a sense of proportion - one is the event, the other is only the effect of the event.' Dida, 34, who writhed around in feigned agony in the goalmouth when he was barely tapped by the Celtic supporter, received no sympathy from the 10-man disciplinary body. Cantamessa said: 'In this decision, logic and balance are lacking. There is the technical (possibility) of a second level of justice - we can get witnesses, develop arguments. We will see.' Celtic chief executive Peter Lawwell was pleased with the outcome, and said: 'As a club we feel this penalty is proportionate to the incident in question and a fair outcome. Unless Milan win their appeal, or unless UEFA themselves contest the independent disciplinary body's decision, as they can, Dida will miss the Italian club's Champions League games against Shakhtar Donetsk. Celtic acted swiftly to punish the 27-year-old supporter, who turned himself in to police and has since admitted a breach of the peace in court and will be sentenced next month. He has been banned by Celtic for life from the club's matches, home and away. Peter Rafferty, president of the Affiliation of Celtic Supporters Clubs, admitted the Scottish club had received a favourable result. Rafferty told PA Sport: 'I am delighted. As far as Celtic football club and the fans are concerned it's a fantastic decision. 'There are always some rumours when these committees get together and one strong one was that the fine could be heavy and another was there could be the closure of the ground. 'That would have been a disaster for the club and the fans. 'But the decision was as good as we could have expected. 'As far as Dida is concerned, UEFA must see that as justice being done and that is a problem for AC Milan.'