The Spanish giants arrive at the Etihad Stadium on Wednesday aware that if they avoid defeat it will end City's interest in this season's Champions League.
Mancini admits there is real pressure on City, but claims they need to embrace big games.
"When you play an important game like this against Real Madrid, there will be pressure but you want games like this. It is important for us to do a good job," he told Sky Sports News.
In theory City could still finish level on points with Real and Borussia Dortmund but he admits this is an unlikely scenario.
"It is possible but I don't think that Real Madrid will not beat Ajax at home, or Dortmund. It was a difficult group when we started and now it is very difficult because we did mistakes in the first two games," he added.
Mancini was asked once again about his troubled front-man Mario Balotelli, who is being strongly linked with a return to Italy, but the City boss remains a huge fan of the 22-year-old.
"Mario, outside the pitch, is a fantastic guy," he said. "Sometimes he doesn't understand which is your job, and how his job is important for his life, but I hope for him that he can understand this quickly."
Mancini even feels that Balotelli has the potential to be as good as Cristiano Ronaldo and Lionel Messi.
"Now he is 22 but life can go quickly and I hope he can improve everything because as a player he could be like Cristiano and Messi," he said.
"If he understands that to be like this you should work hard, your mind should be always on your job, not on the other things that are not important. I am very sorry for him for this.
"He has everything to be one of the best players in the world."
Mancini remains hopeful he can oversee Balotelli's development into the player he believes he could become.
"It is not too easy to work with him every day because if you are a manager, you should manage 22 players," he said.
"This is difficult sometimes but I hope he can change his mind."
A back injury sustained on recent international duty prevented Balotelli from returning to the side in Saturday's 5-0 Premier League win over Aston Villa and he remains a doubt for the Real clash.
"He will train with the team and we will see if he can play," said Mancini.