Inter need to avoid a collapse in the second leg of their all-Italian tie in order to reach a clash with either Real Madrid or Manchester City in Istanbul.
And Inzaghi was in confident mood after watching his team dominate the first leg, missing several chances to make the scoreline humiliating for their cross-town rivals.
"We played a brilliant first half, but it's a tight scoreline for what we did out there," Inzaghi told reporters.
"Then in the second half we managed the game well. Apart from (Sandro) Tonali's shot (which hit the post) the boys did great in covering the whole pitch.
"It's a hugely positive night which gives us a lot of satisfaction but we're missing one more piece to attain a dream that we believed in since August.
"There are still seven days left. We know we've got one more small step to go."
Milan could have star man Rafael Leao back for Tuesday's second leg after the Portugal winger missed Wednesday's match with a thigh injury.
Leao is crucial to Milan's attack and his absence made Inter's job that much easier, but Inzaghi isn't worried about the 23-year-old's potential return next week.
"We have played loads of derbies with Leao playing and without him playing," said Inzaghi.
"He's a great player who is very important for them but it won't change our plan for the match."
Milan coach Stefano Pioli said that his team still believe that they can turn the result around on Tuesday despite the two-goal deficit and having to play as the nominal away side at the San Siro.
"I know my players, I know we can do better... next week's match will be psychologically very difficult for both teams because we have the chance to reach the final," Pioli told reporters.
"We have the chance to score some goals, put them under pressure and set right what's happened.
"It's difficult, it won't be a walk in the park. It will be difficult but we have to believe because football has taught us that you can overcome all sorts of obstacles."
