Jose Mourinho's side have virtually given up hope of defending their league title after an erratic campaign, leaving their quest for a 10th European crown that has eluded them since 2002 as the overwhelming priority.
They are still alive in the King's Cup and play at Barcelona in the second leg of their semi-final on February 26 with the arch rivals also tied at 1-1 after last month's first leg in Madrid.
Four days later, they host Barca at the Bernabeu, this time in the league, and then have only three days before they take on United with a place in the quarter-finals of Europe's elite club competition at stake.
Barca are 12 points clear of second-placed Atletico Madrid at the top of La Liga, with Real a further four points behind their city neighbours in third.
There has been widespread speculation that Mourinho will move on at the end of the season whether Real win the Champions League or not but elimination at the hands of United and his old rival Sir Alex Ferguson as well as a Cup reverse to Barca could hasten the Portuguese's exit.
"I am not feeling any pressure," Mourinho said at a news conference after Wednesday's showdown at the Bernabeu.
"I do serious work, I give my all and I go home satisfied with what I have done and with my head held high," added the former Chelsea and Inter Milan manager.
Asked whether his future in Spain depended on the United tie, he said: "I have no idea and I am not concerned.
"Both results in the cup and the Champions League [first legs] are 1-1 but Real Madrid can score goals and win matches away from home."
Real will have to defend better from corners if they are to get past United and Mourinho singled out captain Sergio Ramos for criticism after he let Danny Welbeck spin away from him and head into the net for Wednesday's opening goal.
Cristiano Ronaldo, playing his first match against his former club since joining Real for a world record fee in 2009, equalised with another header.
"We train, we organise ourselves, we define each player's role, we watch videos of our opponents to single out their strengths in dead-ball situations but when you lose the individual duals there is nothing you can do," Mourinho said.
Ramos, who was lucky to be on the pitch after appearing to strike United defender Jonny Evans with an elbow in the first half, admitted his error.
"I am realistic, he [Welbeck] got the better of me," the Spain international told reporters.
"But I prefer to focus on the attitude of all our players," he added.
"We are optimistic about the game at Old Trafford. We will go there with the same mentality, convinced that we can win.
"We know that we have to go there to win, although we know that Manchester are a great rival and we have to respect them."
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