City, on top for much of this season, are now one point behind local rivals and reigning champions Manchester United with 10 games left following their defeat by Swansea last weekend.
That 1-0 loss came at the end of a week in which City were defeated by the same scoreline in the first leg of their Europa League last 16 clash against Sporting Lisbon in Portugal.
Now doubts have started to surface as to whether City -- bidding to be crowned champions of England for the first time since 1968 -- have the staying power to deny United.
However, Mancini, speaking ahead of the second leg against Sporting, said Wednesday: "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 (destiny) 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 fan was pictured crying after the loss to Swansea at the Liberty Stadium and Mancini said his side were well aware of what lifting the Premier League trophy would mean to the club.
"We want to win the title, to do history for the club," he added.
"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."
And Mancini insisted a side without injured captain Vincent Kompany had not had their confidence dented.
"We are positive and we think we will win the 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."