City are the favourites for the clash as they chase a treble having won their fifth Premier League title in six years and the FA Cup.
However, Inzaghi's side are in good form themselves, having won 11 of their last 12 matches in all competitions. The Italian labelled City the strongest team in the world but said that his players were ready to cause an upset.
"We know we have a huge opportunity to write a page in football history," Inzaghi told a press conference.
"We know it will be very difficult but we will try. Together is the word that brought us here and together we will try to win on Saturday.
"We know the type of match we'll have to play tomorrow. City are the strongest team in the world, they proved it in the matches they've played.
"We're proud to have come this far, we'll do everything to play a game of incredible concentration. We'll have to limit our mistakes and seize the opportunities we have."
Inter, who have won the European Cup three times before, have already secured the Coppa Italia and Supercoppa Italiana this season and will use their experience of winning tough against City.
"Tomorrow we will play our 57th game this season, it was a very long journey with some difficult moments. It's in those that we've grown the most," Inzaghi said.
"We've learned from deserved and undeserved defeats and put in a crazy effort to arrived in Istanbul.
"The last few weeks we have had little time to think about the Champions League final, we had the Italian Cup final that we cared about very much.
"Only now are we understanding what we have achieved so tomorrow we will fight inch by inch on the pitch to come out with the win."
Inzaghi added that although the midfield battle will be key on Saturday, the mentality of his players would be more influential.
"(The midfield) will be very, very important. But I think the legs, the head and the heart will be even more," Inzaghi said.
"The legs will be used to run, the head to be lucid, the heart to find energy that in some moments you don't think you have. We will try to play one of those matches that need to be played in a final."
