The Premier League winners must beat the Spanish giants in their Group D clash at the Etihad Stadium to retain just a slim hope of reaching the knockout stages.
Even then they would need to follow up by beating Borussia Dortmund in Germany in a fortnight and still hope other results went in their favour to progress.
Mourinho says that is not going to happen and feels that must be damaging for a team that should be capable of winning the Champions League.
The former Chelsea boss said: "I think they are a team to win the competition - one of the teams to win the competition.
"I think it is normal if a big team doesn't win the competition because there are other teams with the same power, desire and responsibility, and only one can win.
"I don't think it is normal when you are out of the competition at the very early stage.
"I speak for myself. If Real Madrid loses a final or semi-final, or even a quarter-final, that is football.
"When you are out at the group phase it is more difficult to accept and understand.
"Last season they are out, and I think this season they will be out again.
"I think they can win tomorrow [Wednesday], of course they can, and they can also win in Dortmund, why not, but eight points is not enough."
City boss Roberto Mancini knows his side's hopes hinge on containing the "incredible" Cristiano Ronaldo.
The prolific Portugal forward will make his first return to Manchester since leaving United three years ago as Real Madrid visit the Etihad Stadium in the Champions League.
It is a match City must win to retain any hope of qualifying for the knockout stages from Group D.
Ronaldo, 27, is at the height of his powers and has scored a remarkable 165 goals in 162 appearances for Real, including the late winner when they met City at the Bernabeu in September.
Mancini is well aware of his threat, even without taking into account any extra incentive from playing back in Manchester.
Mancini said: "I think (it is) not only tomorrow [Wednesday] night - I think Ronaldo has a big impact on every game.
"One player that scores every game, one or two goals, is an incredible player. For this reason we should have more attention on him because he is a player that can change the game."
City have collected just two points from their first four matches in the competition and are almost out of the reckoning.
Real will have plenty of reason to push for a result themselves as they trail group leaders Borussia Dortmund by a point and must shake off any late charge from Ajax or City.
City striker Carlos Tevez knows all about Ronaldo having played alongside him at Old Trafford.
Tevez said: "Cristiano is one of the best players in the world and he will play in this game the way he always has done.
"He does not seem to feel pressure, and there will be no added pressure just because he is back in Manchester.
"Once he gets a chance to face up to you and run at you with the ball he is very, very dangerous and he strikes the ball well too."