The reigning Premier League champions head into Monday's derby trailing the top-of-the-table Red Devils by 15 points, having won just 18 of their 30 top-flight games this term.
In contrast, United are unbeaten since November and have won 25 of their 30 Premier League games - and Mancini says teams are intimidated by Sir Alex Ferguson's charges.
"No-one plays well against United because they only play with fear," Mancini is quoted as saying by The Daily Mirror. "United are strong now because of this importance as a team, as a club.
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"This is normal, this is football, this is because United is a strong team for a long time. For the other teams they play against, it is difficult. We are young as a team. We don't have the same importance like United in this moment. Maybe in 10 years it will be the same. The history is very important."
A win for United on Monday will open up an 18-point gap with just seven games of the season left to play, and Mancini has rued failures in the transfer market to a slip in standards from last term.
The Italian believes his team would have fared much between domestically and in Europe if he had had more success with recruiting his desired new personnel.
"Probably we would be on top, could win the second title and probably we would be in the Champions League quarter- final," Mancini said.
"We had a chance to get three or four players who could improve our team but we didn't in the end. Now it's finished.
"Last year we played really well because we scored a lot of goals. But this year the only difference is the goals we didn’t score. If we’d scored maybe 15 goals more, probably we would be on the top.
"We've been missing important goals in games we deserved to win easy. We lost a lot of points because we didn't score enough goals. This is the difference. We also had a lot of injuries."