Milan are flying going into the game after their Champions League win over Barcelona.
"The credit for Wednesday's game goes to the players, but tomorrow is a different game, both for Serie A and the city," said Allegri.
"It will be different in tactical and technical terms too. Inter will be eager to make up for recent problems. We must remember that up until a few weeks ago they had a 13-point advantage over us, so it's going to be tough.
"Inter have absentees, but also a big squad with a lot of quality, so we have to respect them. The Derby is a special game that is separate from the rest of the season and we know that we've got to emerge with a positive result."