Mancini has signed Yaya Toure, David Silva, Aleksandar Kolarov and Jerome Boateng this summer and is close to signing Mario Balotelli.
City have not won a major prize since 1976.
“I will win a trophy,” Mancini declared. “I don’t know if it will be the Premier League, a European trophy or the FA Cup.
“But we will win something. This year we will change our history.”