"As I have always said and as I continue to say, today I am Inter's first fan," Conte said. "I don't sleep because of Inter, I give my all, as I have done in the past with Chelsea, Italy and Juventus.
"I don't have to be accepted by anyone. I just want the people to understand that I will give my all while I'm here, right until the end, as I have done in the past." Both teams had a goal ruled out in the first half and Inter hit the woodwork. The Nerazzurri broke the deadlock shortly after the interval with a deflected strike from Marcelo Brozovic.
Romelu Lukaku all but sealed the result in the 78th minute with his third goal in four Serie A matches. "How much there is of me in this team I don't know," said Conte, who steered Juventus to the first three of its eight successive league titles. "Certainly in the negative situations I always assume responsibility. Today was positive and it's right to give the credit to the guys.
"These are matches that if you want to win you have to show that you have more desire ... This has to make us understand that if we want it we can do it." Milan only mustered one shot on target all match and had goalkeeper Gianluigi Donnarumma to thank for keeping the scoreline down.
But Milan coach Marco Giampaolo insisted there was only "a slight difference" between the two teams. "The slight difference between us is experience," he said. "But we managed to reduce the gap after the first 10-15 minutes.
"I think the match was mainly balanced but we didn't manage to react after they scored the goal." As part of the anti-racism initiative launched by Milan this week, the two teams emerged mixed together at the San Siro.
Both teams had conceded just once heading into the derby but Milan almost gifted Inter an early goal through a poor backpass by Ricardo Rodriguez but Donnarumma was sufficiently alert as Lautaro Martinez tried to pounce.
Donnarumma also came to Milan's rescue shortly afterward as he got down smartly to deny Lukaku with a one-handed save. Inter went even closer two minutes later when Donarumma could only parry Lautaro's effort but Danilo D'Ambrosio volleyed onto the right post from point-blank range.
It was Milan which thought it had taken the lead in the 23rd minute through Krzysztof Piatek but play had already been halted for Franck Kessie's handball. Inter also had a goal disallowed. Donnarumma pulled off a sensational save to keep out an equally impressive overhead attempt from D'Ambrosio and when Lautaro tapped in the rebound he was flagged offside.
Inter did break the deadlock four minutes after the break as Stefano Sensi sent a quick free kick through to Brozovic, whose effort through a crowded penalty area was deflected in by Rafael Leao. Milan never really looked like equalizing and Inter doubled its tally when Lukaku headed Nicolo Barella's cross into the top right corner.
Inter almost scored a third in stoppage time but Antonio Candreva's shot came off the left post and rolled across the face of goal.
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