Tiemoue Bakayoko exchanged his jersey with Lazio defender Francesco Acerbi at the end of the game but then, with team mate Franck Kessie, waved it triumphantly in front of Milan fans in the Curva Sud in a gesture which generated widespread criticism.
The incident happened as scuffles broke out among players following the match which was a key battle in the race for Champions League qualification.
Gabriele Gravina, the head of the Italian football federation (FIGC) was among those who had called for disciplinary action.
"When Acerbi handed over his to the Milan players and shook their hands, he proved he wanted to close any controversy. Exhibiting the same shirt almost like a scalp in front of the crowd was an ugly reaction that we ought to prevent happening again," he said on Monday.
However, the tribunal said on Tuesday that "nothing was reported by the match delegate" and added that it was not a case where evidence from television images could be used. "Therefore, the tribunal is not competent to decide on what happened," it said in a statement.
Kessie, however, was among six players fined 10,000 euros (£8,637) for their part in the trouble.
The others were Andrea Bertolacci and Mateo Musacchio of Milan and Lazio trio Lucas Leiva, Luiz Felipe and Patricio Gabarron.
Bakayoko later phoned Acerbi to apologise and the Lazio defender appeared to accept, when he tweeted: "Enough controversy, we'll see each other on the pitch."
(Writing by Brian Homewood; Editing by Christian Radnedge)
