The Nerazzurri are in the Serie A relegation zone with just one point to their name from their three opening league matches.
Tuesday's 3-1 defeat at Novara, Inter's fourth loss in five official games, led to the dismissal of Gian Piero Gasperini.
Ranieri, who is Inter's fifth coach in the last 15 months, is under no illusions about the challenge he faces.
"We've all seen Inter in recent weeks," said the former Roma tactician. "It's a difficult time.
"There have been injuries and bad luck but I am convinced this team has the characteristics to return to winning and return to believing in itself.
"I am not a coach that believes in winning formulas but rather in winning players.
"I believe if a good connection is made between the coach and the players, you can return to win.
"I have asked my players to fight from the first to the last minute."
Inter defender Andrea Ranocchia will serve the first of a three-match ban this weekend.
Ivan Cordoba, Maicon, Thiago Motta, Andrea Poli, Dejan Stankovic and Emiliano Viviano will also miss the trip to Bologna as they are all out injured.
Ranieri has opted to rest Wesley Sneijder in view of next week's Champions League match at CSKA Moscow as the Dutch winger is struggling with a minor thigh injury.
"I prefer not to risk Sneijder on Saturday and have him available in Moscow," he said.
Bologna picked up their first point of the season in Wednesday's 1-1 draw at Juventus and coach Pier Paolo Bisoli expects another tricky test for his side against Inter.
"Inter are coming here wounded," Bisoli said. "It will be a difficult challenge for us.
"With the change of coach they will have found new motivations, as well as new work methods so we must be ready."
Bologna goalkeeper Jean Francois Gillet and striker Alessandro Diamanti are doubtful for the encounter at the Stadio Renato Dall' Ara.
Both players sustained knocks in midweek.
Should Gillet fail to recover, Federico Agliardi will replace him in goal.