The Blues have not won the league since 1968, while their last piece of silverware was the League Cup in 1976.
City's owners have turned the club into contenders for Champions League football, though, with massive investment over the last couple of years.
Mancini feels City now have a strong enough squad to compete for top honours once more but reckons his players just need a bit more belief to establish themselves amongst the game's elite.
"I think the most important thing I try to instil in my players is that they must always believe that they can win - we need a winning mentality at this club because eventually, it pays off," he told the club's official website.
"It doesn't happen overnight and can take maybe six or eight months to really be absorbed, but if you are prepared to work hard every game, you will always have a chance of being successful.
"It's a simple observation but very true - you can't win anything without working hard."
Mancini succeeded Mark Hughes as City boss in December, signing a three-and-a-half-year deal at Eastlands.
The Italian coach led Inter Milan to three successive league titles, while winning the Coppa Italia as manager of Inter, Fiorentina and Lazio.
And now the 45-year-old wants to deliver similar success to the long-suffering City fans.
The Blues reached their first semi-final for 29 years in this season's Carling Cup and finished fifth in the league after being in the race for fourth place all season.
And Mancini feels next term City could be in the scrap for not just a Champions League berth again but the title itself.
"I want to win a lot of trophies with this club," he said. "We did OK this season, but next season I want us to aim to win the Premier League.
"I think our fans are incredible and they have been wonderfully supportive to me since I first arrived.
"It makes me more determined than ever to bring them success - when we win our first trophy it will be a very good moment for everyone, I think."