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Dreary Milan derby points to Napoli title
Captain Lautaro Martinez's first-half header inflicted a fourth successive defeat on the Rossoneri.
Milan failed to register a shot on target and is down in sixth place in Serie A after a miserable winless run was extended to seven games.
The Nerazzurri, on the other hand, are second behind Napoli after a third win in a row, and seeing off its city rival 3-0 in Supercoppa Italiana last month.
While Napoli is likely out of sight with a 13-point advantage at the summit, Inter coach Inzaghi believes a commanding derby display shows his side continues to make strides.
He said: "I'm very satisfied, I complimented the team because they were perfect, I don't remember a derby won and dominated in this way.
"We had a great derby, winning two in I think 20 days don't always happen. We don't look forward or backward in the standings but only at us."
Under-pressure Milan boss Stefano Pioli went with a more defensive line-up in a bid to arrest the champion's slide but Inzaghi's focus was on how his side approached the game.
"There's been talk about it for days [Pioli's tactics]. I have to be honest that I was worried about mine, regardless of how Milan played," he said.
"Every Sunday we meet three or four [man] defences. Tonight in the first half we bordered on perfection.
"In the second we did very well and conceded the first shot in the 75th minute. It's a great satisfaction."
Another big plus for Inzaghi was a substitute appearance for Marcelo Brozovic, the first time the midfielder has featured for Inter since November.