The former Inter coach had a furious exchange with the Nerazzurri captain during the 3-1 win.
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Asked about the bust-up, Conte said: "The match was very tough and heated. There were some arguments. I remember that I brought Inter back to winning ways after 10 years and brought them back to the top.
"Lautaro is a great player, but two two years is too short to get to know a player. I wish him the best..."
The row was sparked after Conte had taken issue with a challenge made by Inter fullback Denzel Dumfries. Lautaro then joined in, miming a scared gesture with his hands, and then a 'talk, talk' gesture directed at his former coach.
The argument continued, and when Lautaro laughed, Conte angrily responded: "Laugh about this, s***!"