City, who have led the table for most of the season, now trail arch-rivals Manchester United by a point with 10 games remaining after losing at Swansea on Sunday.
That 1-0 loss came at the end of a bad week in which City were also beaten by the same scoreline in the first leg of their Europa League last-16 tie against Sporting Lisbon in Portugal.
Mancini wants his team to refocus quickly knowing that, with a game against United still to come, the title is still within their grasp.
The Italian said: "I think that in Portugal and against Swansea we did not play a very good game, we did not play like Manchester City usually play.
"We didn't deserve to lose both games but I think we need to play better.
"We can't cry, now is the time to be strong and keep going. We have a top team and we have time to recover.
"We can't cry because we are one point behind Manchester United.
"We have 10 games, our fortune is in our hands and we can change it if we want to.
"Like we lost points against Swansea, United can lose points against Wolverhampton. Every game will be difficult for both teams."
One City supporter was pictured crying after the loss at the Liberty Stadium and the sight of that has made Mancini extra determined to claim the club's first league title since 1968.
He said: "We want to win the title, to do history for the club.
"We are very disappointed for our supporters after Swansea and I saw on the TV one supporter was crying.
"We want to win for this guy, for all the other supporters. We want to change this.
"I prefer to stay at the top and now we are behind, but it is important to be there at the end of the season. It doesn't change it for us.
"We are disappointed for the defeat against Swansea but now our focus should be about Sporting Lisbon."
City host the second leg against the Portuguese side tomorrow [Thursday].
Mancini has so far given no indication, in words or selection, that he regards the Europa League as a distraction.
It has been suggested since the weekend he may now have to tailor his teams to prioritise the Premier League bid, but he insists he is still going all out for both trophies.
Mancini said: "We can't think negative at this moment.
"We are positive and we think we will win the Barclays Premier League and the Europa League.
"If we thought differently, it would be a mistake. It would be everything to win both competitions.
"We always play with the best team. Even when we change four or five players it is because we have played one game and then another after three days.
"Sometimes these players need to rest - it is impossible the same team can play every game. We have a team of 20 players.
"Tomorrow [Thursday] we want to win and we need to do our best if we want to beat Sporting."
City are hampered by defensive injuries for tomorrow [Thursday].
Captain Vincent Kompany is unlikely to return from his calf problem before the trip to Stoke on March 24 and right-back Pablo Zabaleta is still out with a hamstring injury.
Joleon Lescott has a chance of making the bench as he recovers from a groin injury, but midfielder Gareth Barry has suffered further discomfort from a back problem and could be rested.
Barry appeared to show dissent when controversially substituted in the first half on Sunday, but Mancini says he has a fitness issue dating back to last month.
Mancini said: "Gareth has had a problem with his back for 20 days. He can't run well.
"When he went to the national team he had a problem.
"On Sunday he didn't play well but I think that is because he had a problem."
Another player who will not feature tomorrow, because he is not eligible, is striker Carlos Tevez.
But the Argentinian, who has been training for the past month after ending his dispute with the club, could be back in contention for next Wednesday's clash with Chelsea.
Mancini said: "We will see in the next week. It depends on Carlo.
"If Carlo is okay then probably, but it depends on a lot of things."