The Rossoneri, out of the title race in Serie A and not competing in Europe this season, know the Coppa is their only chance of silverware.
Saturday’s 3-1 Serie A defeat at Lazio followed their 1-0 loss against Atalanta and dropped Milan to 10th in Italy’s top flight.
“We are going through a difficult time,” AC Milan striker Jeremy Menez told his club’s official website. “We have to bounce back and try to get a positive result tomorrow.
“It’s true that tomorrow’s game is very important for us, for the coach and for our fans.
“We are all behind Inzaghi.
“We are not doing well in the league and if we can do something in the Coppa, it would be beautiful.
“But we cannot make a mistake against Lazio and we have to show hunger and determination from start to finish.”
Milan have not won the Coppa since the 2002-03 campaign.
Lazio coach Stefano Pioli will be forced to make changes to the side.
Serbian striker Filip Djordjevic fractured his right ankle during Saturday’s game and will undergo surgery on Tuesday.
Victory at the Stadio Olimpico on Saturday saw the Biancoceleste climb to third in Serie A.
Twenty years have passed since Juventus last lifted the Coppa and Massimiliano Allegri’s men will be looking to take one step closer to reaching the final by beating Parma in Wednesday’s quarter-final.
The Turin giants head to the Ennio Tardini stadium on the back of Sunday’s 2-0 triumph over Chievo, their third straight league victory.
That outcome, coupled with Roma’s 1-1 draw at Fiorentina, allowed Juve to move seven points clear of the Giallorossi at the top of the standings.
“There are still many games left to play until the end of the season,” Allegri said. “We just have to be calm and take things one step at a time.
“Now our focus is on an important game at Parma. We have the duty to arrive to the semi-finals of the Coppa.”
Parma go into the contest with coach Roberto Donadoni having received a vote of confidence after Sunday’s 2-1 loss to Cesena.
The defeat, Parma’s 16th of the league campaign, dropped Donadoni’s side to the foot of the standings, 10 points adrift of safety.
“Donadoni has all of our trust,” Parma president Ermir Kodra told the Italian press. “He will remain in charge.”
In the other quarter finals, Roma host Fiorentina on February 3 and one day later Inter MIlan travel to the Stadio San Paolo to face Napoli.