Mancini hopes to reduce United's 12-point advantage at the top of the Premier League before the sides meet at Old Trafford on April 8, but he knows it will not be easy to claim all three points at Goodison Park.
City have lost five of their last seven against the Toffees and played out a 1-1 draw with them at the Etihad Stadium in December.
Mancini said: "Every game against Everton is very hard. It is difficult because Everton are a top team, they play always 100 per cent.
"They are strong, they have good players and a good manager. They always play well against top clubs.
"If you want to beat Everton, you should be ready to fight in every position.
"They work hard as a team. For every team it is difficult against them. Saturday for us will be important."
The Everton game is a lunchtime kick-off with United hosting struggling Reading in the evening.
Mancini added: "The next two or three games will be crucial. If they lose a point in the next two games - maybe.
"After the two games, we have the derby. But it all depends on us. When you are behind you should win every game.
"We hope we can play a derby with nine, seven points, maybe 10. Less than 12 would be better.
"From the derby to the end of the season, they have three or four difficult games."
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