Sir Alex Ferguson’s side face Blackburn Rovers on Monday before hosting QPR the following Sunday, while City face a trip to Arsenal later that same day.
Should United win both games, the champions can move eight points clear of City before they kick off against Arsene Wenger's side at the Emirates.
“If we go eight points behind then it is finished,” Mancini told reporters.
“It’s clear we are disappointed. We have made some mistakes, me and the team. We have also been unlucky, like losing three or four key players at an important moment.
“But when you are a strong team you should be able to pass these difficult moments. Yet football can change in two or three games.
||Manchester City are 10/3 with Bet365 to win the Premier League this season
“I had an experience in Italy with Inter Milan when we were five points behind with five games to go yet we still went on to win the title.”
However, captain Vincent Kompany has insisted that City are still in with a shout of the title despite United’s advantage.
“We’d have to finish the job by beating them [United] at home," he said.
"We’ll still keep believing, it’s just not as easy as it was."
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.