The reigning champion, which secured the league title in dramatic fashion last season, has struggled over the festive period this term, needing a late goal to beat Reading over the weekend before falling to a 1-0 defeat to Sunderland on Boxing Day.
The Red Devils also scored late on to secure victory over Newcastle on Wednesday, extending their lead at the top of the table, but things could be even worse for City had Sir Alex Ferguson's men not drawn with Swansea beforehand.
Mancini indicated that he is still calm despite the large gap, acknowledging that their rivals have the upper hand but insisting that his players will have "no problem" in catching up. Last season, City made up an eight-point gap in the final six games of the season to win the league crown.
"United are better than us but it can change," Mancini told reporters. "They are on the top but we have the time to recover. Seven points are no problem."
Critics have suggested that Joe Hart should have saved Adam Johnson's low shot that handed the Black Cats victory on Wednesday, as the effort slipped under his grasp. Mancini defended his goalkeeper, who he declared was not to blame, and instead praised the former City attacker for his inventiveness.
"Johnson was really clever, because we all thought he was going to cross," Mancini said. "Instead, he shot. He did very well. I do not think Joe Hart was at fault."