City are still able to qualify from their Champions League group, despite winning just once so far, but must be victorious in their two remaining games, and hope that los Blancos are unable to pick up another point.
Mancini saw his side dismantle Aston Villa 5-0 on Saturday, but has urged his players to move on from that and focus on the Liga champions.
"This was a really good performance and result but it will count for nothing against Real [Madrid]," the Italian told The Daily Mail.
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"We went close last time, in Madrid, and were 2-1 up with four minutes to go, but this is not going to be easy.
"It is a different game, and if we want to beat them, we will have to defend very well. They have three or four players who can decide a game at any moment, and we are going to have to work very hard as a team."
The Premier League champions have improved defensively in recent weeks, keeping three clean sheets in their last four domestic games, but Mancini has challenged his leading lights in attack to make the difference against Cristiano Ronaldo and Co.
"At least we have improved defensively in the last four or five games, which is important," he said.
"It is down to the whole team playing different football and having 65 per cent, or more, control of the game. That has helped us look more solid.
"If you have players who have won World Cups, like David Silva, or who have won everything in the game, like Yaya Toure, you know what you are going to get on nights like this.
"For them, playing against Real Madrid is the essence of football, and it should bring the best out of them.
"When you are young and starting out in football, you think about how much you would love to play against Real Madrid or Barcelona.
"Sergio Aguero is the same, and it could be important that he missed the game in the Bernabeu. He will want to make up for that and I think he can cause problems for Real [Madrid]. But, above all, we must play as a team.
"They have a big history, going back a long way. But I do think we have the players who can beat them. It is possible."