The holders gave a thrilling attacking performance at the Nou Camp and had their arch-rivals hanging on for the final whistle as they came back to draw 2-2 before falling 4-3 on aggregate, just one goal away from progress to the semi-finals.
The offensive line-up, the asphyxiating pressure on Barca's playmakers and their never-say-die spirit were a stark contrast to their poor showing in the first leg, which led to the first serious signs of protests against Mourinho's stewardship.
"Madrid shrugged off their recent complexes and were a centimetre away from a monumental achievement," the sports daily Marca said on Thursday.
The pro-Barcelona daily Mundo Deportivo wrote "It was a two-legged tie and Barca knocked out Real at the Bernabeu."
Real fans had been unhappy with what they perceived as Mourinho's timid and defensive-minded tactics in the first leg.
Playmakers Mesut Ozil and Kaka, who started on Wednesday, were left on the bench last week, while newspaper reports of a divided dressing room added to the club's frustration at their inability to overcome the European champions.
Former Chelsea and Inter boss, Mourinho, has only managed one win over Barca in 10 attempts, but it was the manner of the defeats which particularly hurt Real followers.
"[Fans] won't whistle him for defeats like these," El Pais wrote on Thursday.
"Barca played badly and Real played well. Luck turned its back on Mourinho, but the game revealed the way to combat Barcelona."
Real defender Alvaro Arbeloa told reporters: "We have ridden ourselves of this block that we had when we played against them."
JOIN THE PARTY
Once again, Real finished a match against Barca with 10 men after Sergio Ramos was sent off near the end, and visiting players crowded the referee to complain at the final whistle.
Under Mourinho, Real have had seven players sent off in 10 matches against Barca and the Portuguese has regularly accused officials of favouring their rivals.
"I heard players saying in the dressing room it was impossible to win here," Mourinho said afterwards.
Real and Spain goalkeeper Iker Casillas told referee Fernando Teixeira Vitienes to go and join the party with the Barcelona team as he left the pitch.
"Yes, I did say that, but it was in the heat of the moment," Casillas said. "We deserved much more. We are sad but pleased that we have put in a good performance. You can see it is much more even between us now."
Barcelona defender Gerard Pique dismissed the complaints: "The referees make decisions which can help or go against both sides."
The Madrid-based daily As said it was wrong for the club to seek excuses in the refereeing, and had words of advice for Mourinho, who's side top La Liga by five points from Barca, and who still have to visit the Nou Camp in the league this season.
"Th
