City put aside their recent Barclays Premier League frustrations to brush aside Championship outfit Leeds and ease into the FA Cup quarter-finals with a 4-0 win at the Etihad Stadium.
Having fallen 12 points behind Manchester United at the top of the table, the knockout competition now appears to represent City's most likely source of silverware but Mancini is not ruling anything out.
The Italian said: "In Italy, you say a game like this is like brodino soup, a starter.
"I hope it can help us to start to win in the Premier League."
Mancini was angry and heavily critical of his players after their damaging 3-1 loss at Southampton last week.
There was no danger of a repeat of that performance as Yaya Toure set City on the way to a convincing victory after just five minutes.
Sergio Aguero soon added a second from the spot and capped a superb individual performance with a fine strike on 74 minutes after setting up Carlos Tevez for the third early in the second half.
City now host Barnsley in the last eight and Mancini said: "I am happy because it was important to win after Southampton.
"Every game in the FA Cup is difficult if you don't have a good approach.
"We started very well. Very quickly we scored two goals and after that it was easier."
To have any hope of reigniting a title challenge, City will probably need to beat third-placed Chelsea next Sunday.
Mancini said: "This is possible but I think we should be confident, always.
"We lost seven points in three games - this can happen for every team. We play a lot of games.
"I think in this moment they (United) deserve to be there because they played better than us. They scored more goals than us."
Leeds now return to their Championship campaign and their laboured efforts to claim a place in the play-offs.
Neil Warnock's outclassed side lacked bite throughout and their fans viewed the hammering with a self-deprecating humour which barely concealed their true feelings about the manager and the team.
Warnock was told it was "time to go" while the club's uncertain off-field picture continues to add to supporters' frustrations.
But Warnock is not hiding from the situation and, with his contract running down, accepts his tenure could end ingloriously.
He said: "If we don't go up, I won't be there. I think the fans knew that all along.
"There's no way I want to stay in the Championship again next year."
When asked if a change could be made sooner by the club's new owners, Warnock said: "It's their prerogative.
"If they think it will help them then I am not against it. I am a bit old in the tooth.
"What has gone on behind the scenes in the last 12 months, I think I deserve a medal."