Trailing 5-2 after the first leg of their Champions League semi-final, Roma need to score at least three goals at the Stadio Olimpico on Wednesday to reach the May 26 final in Kiev.
Dzeko scored a crucial, late away goal in the 4-1 quarter-final first leg defeat at Barcelona and the opening goal of Roma's 3-0 second leg win at the Stadio Olimpico that saw the Italians through on away goals.
The Bosnian handed Roma another lifeline with an 81st strike after Liverpool had romped to a five-goal lead at Anfield last week, Diego Perotti adding a precious second from the spot four minutes later to keep Roma's final hopes alive.
"Players with his (Dzeko) qualities must be decisive as (Mohamed) Salah was in the first leg," said Di Francesco.
Former Roma forward Salah tore through his former club at Anfield, scoring twice and setting up two more goals.
"We can't change a team just for him (Salah) or put three players on him, we have to be good at raising the athletic level, giving little, but remembering that we have to score three goals.
"We were at the mercy of Liverpool for 25 minutes and that cannot happen. We want to try and do something big in a stadium with 70,000 people.
"If I could, I would copy and paste that performance against Barcelona, not just technically but on a mental and physical level," he added, of their comeback from 4-1 down against the Spaniards last month to reach the semi-finals.
"The desire to make another miracle happen must push us all to give that extra something."
Bosnian forward Dzeko has scored 24 goals this season for Roma in all competitions, and Radja Nainggolan warned he was ready to break his European drought.
"I've never scored in the Champions League, maybe I'll break through tomorrow," said the Belgian.
"We will try to complete another comeback, and although it will be complicated I'm the type of person who never likes the simple way."
Dutch defensive midfielder Kevin Strootman however has been ruled out with a leg injury.
Roma lost the European Cup final to Liverpool 34 years ago, but Di Francesco warned: "The 1984 final is in the hearts of the people, but they are two games that cannot be compared."
Liverpool manager Jurgen Klopp's assistant Zeljko Buvac stepped aside this week for personal reason, and Di Francesco joked: "I've kicked out my assistant too to make it even!
"It's internal stuff, I'm not preparing the game based on that. We'll face a strong and determined team which represents a great club, one with a great history in Europe.
"I don't think one staff member can make a difference."
Off-pitch tensions are also high as Liverpool supporter Sean Cox lies in a coma after being attacked before last week's first leg in Anfield.
"There are bad apples among all fans," said Di Francesco. "I've already said that I stand shoulder-to-shoulder with Sean Cox and his family and I'm against all forms of violence, like we all are here.
"There are good fans in Rome, we can't allow a small number of fans, which I think there are in England too, to ruin our beautiful sport.
"I want to make an appeal, it must be a joy to come to the stadium tomorrow."