Mourinho was hired from Inter Milan three years ago to help Real win the 10th European crown that has eluded them since 2002 but the La Liga side are on the brink of a third straight failure at the last-four stage under his stewardship.
"In practically all football clubs success belongs to everyone but failure is always the fault of the coach," the Portuguese told a news conference on Monday.
"I am perfectly calm because I know that is the situation.
"There are fantastic coaches in football who have never won the Champions League, I have won two, for which I must thank God. But I will continue to fight for a third."
Mourinho, who won Europe's elite club competition with Porto in 2004 and Inter in 2010, again had to answer a host of questions about his future amid speculation he will leave Real at the end of the season despite having a contract until 2016.
He has so far refrained from committing to staying beyond June and said this month a decision on his future would be taken at the end of the campaign.
Some reports have said he is poised to rejoin Chelsea, where he failed to win the Champions League, and that Real had lined up Paris St Germain coach Carlo Ancelotti as a replacement.
"If you want to know about contacts between Real Madrid and Ancelotti you have to ask Madrid not me," Mourinho said.
Asked whether Tuesday's game could be his last home match for Real in the Champions League, he added: "I feel that this could be the most important match for Real Madrid in the last 10 years.
"But I felt the same thing before we played in Dortmund and we played there as if it was a friendly."
He also shot down a report that he had told Dortmund coach Juergen Klopp he was moving to Chelsea at the end of the season. Klopp has also said the report, in Germany's Bild newspaper, was untrue.
"The truth is that I did not speak to Klopp about my future, and Klopp can only speak the truth, nothing more," he said.
"It's a shame that people read the newspapers and then don't listen to what Klopp said."
Mourinho said he was not surprised that Dortmund, who won the Champions League in 1997, were challenging for another European crown.
He predicted a bright future for the club despite the imminent departure of midfielder Mario Goetze for Bundesliga rivals Bayern Munich and the possible exit of striker Robert Lewandowski, who scored all four of Dortmund's goals in last week's first leg.
"I have thought Dortmund were a candidate to win the competition from the beginning of the season," Mourinho said.
"Last season they had a year of adaptation when they were not successful in the group phase but it's not a surprise to me that they are where they are.
"They are going to lose Mario Goetze and it is said they are also going to lose Lewandowski.
"But it seems to me that they have a great team structure and a great set up to allow a coach like Klopp to do his work in a very calm atmosphere.
"I am sure they will find replacements to ensure continuity because the team is extremely good and so is the coach."
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