Celtic chairman Brian Quinn has accused Dida of play-acting while condemning the fan who confronted the AC Milan goalkeeper on the pitch in Glasgow.
Dida was carried off the park after the incident
Uefa is to investigate the incident near the end of Celtic's 2-1 victory in Champions League Group D.
And Quinn told BBC Sport: "I'm making no excuses for the behaviour and the fan behaved disgracefully.
"But the contact made with the goalkeeper was minimal. His antics have to be taken into account as well."
The supporter ran on to the pitch following Celtic's late winner against the European champions and appeared to tap Dida on the shoulder as he ran across the six-yard box.
Dida initially gave chase to the fan before falling to the floor - and was carried off on a stretcher holding an ice pack to his face.
There are precedents for the same kind of incidents
Uefa communications director William Gaillard
"All I saw were the TV pictures," said Quinn. "He took a couple of steps after the fan and then obviously made this decision that he should go to ground.
"Unless I missed something, he was carried off on a stretcher for what seemed to be the lightest tap you can imagine."
The fan disappeared into the crowd in the aftermath of the celebrations.
But Quinn confirmed that the Scottish champions would investigate how he had been able to run on to the pitch and could even sue the fan involved.
Milan officials say they will not seek a replay of the match.
"We spoke to the officials of Milan, they were not ranting and raving, they were being sensible," said Quinn.
Uefa communications director William Gaillard said the governing body expects to receive their match delegate's report by the end of this week.
"One of our prosecutors will look at the document and decide whether to open an investigation," he said.
"If he opens an investigation, it will be a week or two before the disciplinary body deals with the case.
"I don't want to presume anything. There is a whole range of possible punishment. But, of course, there are precedents for the same kind of incidents."
Two seasons ago, Inter Milan were forced to play four games behind closed doors and were fined after a flare hit Dida during a Champions League quarter-final between the city rivals at the San Siro.
The tie was awarded 5-0 to AC Milan.
More recently, Denmark were ordered to play four home Euro 2008 qualifiers at least 250 kilometres away from Copenhagen and fined £41,000 after a fan invaded the pitch and assaulted German referee Herbert Fandel during a match against Sweden in the Danish capital in June.
The match was awarded 3-0 to the Swedes, although Uefa did subsequently agree to slightly relax the restrictions on where future games could be played.
Celtic striker Scott McDonald, who said his winning goal was the highlight of his career, stressed: "I hope the authorities are lenient. It would be a tragedy if what happened affected the team."