Italian believes his side dominated the game at Wembley against Stoke City and fully deserved their victory but warns players they is still room for improvement.
A goal in the 74th minute from midfielder Yaya Toure gave City their first trophy in 35 years and Mancini was thrilled with his team's success.
The Italian's celebrations at the full-time whistle were echoed amongst his staff, players and the thousands of City fans in Wembley as the Citizens created their own piece of history at Wembley, and the manager couldn't hide his delight at their triumph.
"I can only say that I am very happy today, I am happy for all these supporters because after all these years they deserve to win a trophy," Mancini told ITV Sport.
"We dominated the game. We were very unlucky in the first half, the players were fantastic this afternoon. I think we need to improve but today I am very happy."
"Today is a small piece of history for Manchester City. We want to start now."
The cup triumph caps a fine weekend for the Eastlands side after they confirmed their qualification for next season's Champions League in midweek with a 1-0 win over Tottenham.
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