Walter Samuel’s header was enough to give the Nerazzurri the points in the Milanese derby and Stramaccioni later devoted the victory to Inter's ultras.
"The Curva showed their faith in me with a generous banner following the defeat to Siena while others were not so kind," said Stramaccioni.
"These are things that I remember and are important values so this victory is dedicated to my players and to the ultras."
Yutu Nagatomo was sent off for Inter in a game that also saw Milan have a goal ruled out and a penalty claim turned down, the Italian was full of praise for his side’s dealing with the dismissal of the Japanese wing-back.
"I think we did well in two areas in particular. First, the way we approached the game, something we'd worked a lot on. We wanted to begin the game strongly and that was the best start we've made this season in terms of tempo," he added.
"The second aspect which pleased me was how we reacted to being a man light after Nagatomo was sent off. We managed to prevent AC Milan from just playing the ball about on the edge of our penalty area, something they're very good at.
"These are the two most satisfying aspects of our performance tonight. We showed the character of a big club."
Stramaccioni also dismissed comparisons with former coach Jose Mourinho.
He added: "I am not like Mourinho, I am myself. The only comparison that I want with him is that I am a great worker like the president says."