With the title on the line at the Etihad in April, United barely mustered a shot on target.
Mancini said: "A 1-0 is enough for us. They will improve their defensive face. At the start of the season, we had the same problems and we improved. It will be the same for them.
"With the 6-1, they had only 10 players for most of the second half. But in the second derby, we played very well. We did not concede any chances. The second was a true derby because when you have 10 men, it's clear that you have some problems.
"We need to forget what we did last year because it doesn't matter now. But remember if we play like last year, we have a good chance to win."