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City ended their 35-year trophy drought on Saturday after downing Stoke 1-0 at Wembley to clinch a major trophy for the first time since 1976.
The victory was the first tangible return City's owners have been able to enjoy since their 2008 takeover and the subsequent lavish spending on players which has topped £300 million to date.
But while City's players and fans celebrated, Mancini was already looking to future challenges, with next season's Premier League at the top of the list.
"We want to try for the title next year," Mancini said.
"I think this year it was important to start to win. In one week we qualified for the Champions League which was our first target. And we won the FA Cup.
"I think we improved a lot this season, like a team. But I think we need to improve more. We need another step. But it was important that we start to win, because once you start to win, it gets easier."
Mancini believes that City might even have challenged for the title this season had it not been for a fixture congestion which saw them fall away towards the end of the season.
"For two months, we were close to the top. We stayed on the top for four or five weeks. We were very close with Chelsea, United and Arsenal.
"But we suffered in March when we were playing every three days and we had injuries to players. This is impossible. We lost important points for the top. Probably we could have fought for the top."
Most observers expect City - whose qualification for next season's Champions League now makes them a vastly more attractive proposition for elite talent - to spend big once again this summer.
The club has already been linked to a mega-money move for Arsenal midfielder Cesc Fabregas, despite the Spanish midfielder's insistence that he would never join another English club if he leaves.
Mancini refused to be drawn on the likely comings and goings at Eastlands this summer.
"I don't know at this moment," he replied when asked if he expected to strengthen his squad.
"I think that now we can only say congratulations to all our players. We have another two games and we want to try and get third place."
Mancini was delighted to see midfielder Yaya Toure repay a slice of his £24 million transfer fee and annual wages which are reportedly £10 million, making him the highest paid player in English football.
Just as he had done in the semi-final victory over Manchester United last month, Toure scored the only goal when he rifled in the winner on 74 minutes.
"We bought him for this," Mancini purred. "We bought him because he's a fantastic player. He scored in the semi-final and now the final.
"But Yaya didn't need to score this afternoon. He's played for many years with Barcelona, with other important teams. He's an incredible player for us. He has a big experience and in the last two games he has showed this."
