City go into today's home game against rock-bottom Reading trailing United by six points.
Ferguson's men earned that advantage with a dramatic 3-2 derby win at the Etihad a fortnight ago. City bounced back with a good away victory at Newcastle.
But Mancini knows that derby triumph for United - ending City's two-year unbeaten home league record - will have given them a massive boost.
He said: "I think that they have more confidence with that victory.
"They also have more confidence because they are used to winning for 20 years. Their mentality is stronger than ours in this moment.
"But, as a team, our quality is the same level. We showed this in the derby. Although we lost 3-2 we showed we were better in that game.
"We have a big respect for United for what they won for 20 years. We need to have respect for them and for Ferguson.
"I don't know if, when I am 70 like him, I can have the same attitude that he has. I have a big respect for this."