City were beaten by arch-rivals Manchester United 3-2, with the Red Devils racing to a three-goal lead at halftime thanks to a brace from Wayne Rooney and a stunning volley from Danny Welbeck.
The opening period was marred by controversy in the 12th minute when City skipper Vincent Kompany received his marching orders for a fairy innocuous two-footed challenge on Nani, a decision which saw Mancini fuming on the touchline.
However, the Citizens showed good spirit after the break, coming out for the second half with all guns blazing, and hit back with goals from Aleksandar Kolarov and Sergio Aguero.
And despite their failure to progress to the fourth round of the competition, Mancini, apart from his anger at Kompany's red card, cut a happy figure at the final whistle, believing the outcome should provide confidence from which his side can go on to win the Premier League title.
"This evening is important for the league," he said.
"Now I think we can win the league because of the character we showed.
"United is a top squad in England. At Old Trafford, with 10 men for 40 minutes, they lost 6-1. Today [Sunday] we played for 80 minutes with 10 players, scored two goals and didn't concede any chances.
"It was a fantastic performance.
"If we have the same attitude and same strength every game, we will win the league."