The duo have been linked with a move away from the Etihad Stadium following a season in which Dzeko found himself in and out of the starting XI and Tevez spent several months on the sidelines after his relationship with Mancini broke down.
Tevez returned to action to play an important part in helping City seal the Premier League title, however, while Dzeko still managed 19 goals in all competitions.
|40/1||Edin Dzeko is 40/1 with William Hill to be top goalscorer in the Premier League this season|
And Mancini has reiterated his desire to fend off reported interest from the likes of Bayern Munich and AC Milan in the two players.
"Both Dzeko and Tevez will stay at City," Mancini told Sky Italia. "We are a great team and we try to keep all our great players. It won't be easy but they will stay here.
"We still lack a couple of players to reach [the level of] Real Madrid and Barcelona. Also our mentality has to grow season by season."
Mancini, meanwhile, dismissed speculation linking him to the vacant Russia job by insisting that he remained committed to the project at City having recently signed a new five-year contract.
"I'm honoured by Russian interest in me, but at Man City there are important plans for the future," the Italian explained.
Mario Balotelli will compete with Dzeko and Tevez for a place in the City team next season having earned praise for his performances at Euro 2012 with Italy.
And Mancini believes the 2012-13 campaign will be a significant one for the 21-year-old as he seeks to put his reputation for controversy behind him.
"Balotelli had to be grateful to himself because of his huge talent," Mancini added. "He must not waste it with non-football matters.
"Next season must be a defining one for him. [Lionel] Messi, Cristiano [Ronaldo] and [Andres] Iniesta work hard every day to stay at top, and he can reach that level."