City's expensively-assembled side lost four of their eight matches in the first month of the year, exiting the FA and League Cups and seeing Manchester United draw level with them on points at the top of the Premier League.
However, the opening fixture of February saw City beat Fulham convincingly, a 3-0 victory maintaining their perfect start to this season of 12 wins from 12 home league games and restoring a three-point lead at the top over United who faced a visit to Chelsea on Sunday.
"I think maybe after tonight something can change for us," said Mancini. "January was not a bad month but a difficult month for us. Now, maybe, we can go the other way.
"The clean sheet was important for the team and it was important to win quickly after the Everton defeat.
"I don't think this puts pressure on United, they are used to always being there on top. But they are like us, we know if we want to win this league we should just try and win all the games and not think about other teams.
"We know we shall have to fight against fantastic teams - like United, like Tottenham - to stay on top so it is important to stay focused on yourselves."
After losing in midweek to Everton, their third league defeat of the campaign, City responded with a dominant victory courtesy of a Sergio Aguero penalty, an Adam Johnson shot, which took a heavy deflection off Fulham defender Chris Baird, and an Edin Dzeko strike.
City's recent indifferent form has not been helped by the absence, at the African Cup of Nations, of influential midfield player Yaya Toure of the Ivory Coast.
City have lost three of the six games for which he has been unavailable although Mancini was pleased with the individual displays of his goalscorers in Toure's continued absence.
"I was pleased with Adam," he said. "It was a good performance. I always thought he was a fantastic player, it is just that he can always improve.
"And I was pleased with Edin and Sergio, not just because of their goals, but because they played for the team."
Mancini confirmed that Samir Nasri was forced off during the game due to a hip injury although the midfielder has an extra day's recovery this week with City not in action until the visit to Aston Villa in Sunday's televised game.
Meanwhile, the Fulham manager Martin Jol confirmed his team hope to have the Russian forward Pavel Pogrebnyak available for next weekend's home game with Stoke after a delay to his work permit.
"He is in the country," said Jol of the player signed from Stuttgart before the deadline. "Hopefully we will have the work permit late in the week, not too late to be involved next weekend. We hope Thursday, it could be Friday."