Ivorian Kessie, 22, and Argentina midfielder Biglia, 33, had to be pulled apart by teammates amid drama on and off the pitch in the “Derby Della Madonnina” between the Milan city rivals in northern Italy.
Kessie, who had been substituted, was furious at something said by Biglia on the bench and had to be held back by teammates as he repeatedly lunged at the Argentine.
“The defeat that hurts me the most was Kessie and seeing what happened on the bench,” said Gattuso, after his team’s five-match winning run in the league was ended.
“That is something I cannot accept with the way I see football, the way I see the team and the group ethic.
“There has to be respect for everyone in the dressing room and it was just unacceptable.
“This means the world to me and that is why it is a double defeat. I will have my say over the next few days,” he warned.
Both players later apologised.
“It was the adrenalin of the match situation, I was frustrated coming off and wanted to do more. I took it out on Lucas and it was a mistake, I apologised afterwards,” Kessie told Sky Sport Italia.
Biglia added: “We feel bad about this embarrassing scene.”
Tensions were also high on the pitch, with Andrea Conti who had come on for Kessie after 69 minutes seeing red for a tackle on Inter striker Laurtaro Martinez, but a VAR review saw the referee change it to yellow, to the fury of Inter coach Luciano Spalletti, who was sent off for dissent.
Matias Vecino scored after just three minutes for Inter, days after his team’s Europa League exit, with Stefan de Vrij adding the second on 51 minutes, to give Inter a two-goal advantage.
For Milan, Tiemoue Bakayoko headed in after 57 minutes with Mateo Musacchio reacting quickly to finish off a rebound (71), just after Lautaro Martinez slotted in the third from the penalty spot for Inter.
“We’ve found the young striker who can put things right for us,” Spalletti said of Martinez.
Inter had also won the reverse fixture thanks to Mauro Icardi’s late winner but the Argentine has not played in over a month amid a contract dispute, which saw him stripped of the captain’s armband.
Inter goalkeeper Samir Handanovic cleared a late Samuel Castillejo header with Patrick Cutrone also denied a last-gasp equaliser with Danilo D’Ambrosio clearing on the line.
Inter leapfrog AC Milan and are two points ahead in third with Roma fifth, four points off the top four who will qualify for the Champions League. Lazio and Atalanta are both two points further adrift in sixth seventh respectively.
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