Inter thrashed their city rivals 5-1 at San Siro on Saturday.
“We scored goals at the right moments," said Inzaghi.
“And the substitutes did very well right in the moment after we had conceded the goal for 2-1.
“Congratulations to the guys, we're very satisfied but this is only the start. We know how much the whole Inter family cares about this derby."
Of Henrikh Mkhitaryan, Inzaghi said, “We all know who Mkhi is. I don't bother listening to or reading much.
“I just watch my players, what they do in training.
“I was a bit worried because with the first three matches, we had a whole week to prepare. And this time around, some of my players had been away with their national teams.
“The South American internationals only returned 24 hours ago. But they showed that they know how to play in these matches."
Inzaghi also said of striker Marcus Thuram, “Marotta and Ausilio already wanted to sign Thuram in January.
“And I had also spoken with Deschamps, who spoke highly of him. A player with great quality and a guy who we all immediately fell in love with.
“Great signing. Well done by the club, who had already been following him for twelve months."