The former Galatasaray boss replaced Walter Mazzarri at the Nerazzurri helm on Friday, after the outgoing coach had overseen an inconsistent start to 2014-15.
Mancini, returning to the club he coached to Scudetto glory between 2004 and 2008, wants a quick turnaround in form to see his team move back towards European qualification places.
"We must get to work without wasting time," Mancini said to Corriere dello Sport.
"I am sure the team is competitive, but superior to that which it shows in the league today. We can do it."
Although the Italian expects the job at San Siro to be tough, Mancini is delighted to have returned to the club where he forged a successful career before taking on the Premier League as Manchester City coach.
"I am happy to be back in a club I consider my home," he added. "Inter and their fans have always remained in my heart.
"I'm ready for a challenging and rewarding adventure. First up, we have the derby against AC Milan and then the match against Roma, one of the favourites for the title."Mancini's first game back is officially an away game, but, as AC Milan share a stadium with Inter, it means that he will be thrust back into San Siro on Sunday November 23 before his first continental tie at home to Dnipro four days later.