After falling behind to a 17th-minute Franck Ribery strike in the semi-final first leg in Germany, Real battled back to 1-1 when Mesut Ozil tapped in what could prove a priceless away goal eight minutes after the break at the Allianz Arena.
Instead of going in for the kill, Mourinho appeared willing to settle for a draw and hauled off creative pair Ozil and Angel di Maria, replacing them with full-back Marcelo and defensive midfielder Esteban Granero.
It might have worked out, securing a slight advantage for next week's second leg in Madrid, but for another dreadful performance from Mourinho's Portuguese compatriot Coentrao, for whom Real paid Benfica 30 million euros.
Coentrao was unable to cope with tricky Bayern forwards Ribery and Arjen Robben and allowed Philipp Lahm to skip past him and cross for Mario Gomez's 90th-minute winner, sealing Real's first defeat in Europe's elite club competition this season.
"The 30-million-euro full-back saved the best until last [against Bayern] when he was very late closing down Lahm, who was able to cross under no pressure for Mario Gomez to score," the paper wrote sarcastically.
Coentrao's team-mates preferred to focus on the positives from Tuesday's game as they prepared for Saturday's La Liga 'Clasico' at bitter rivals Barcelona.
Centre-back Pepe, another Portuguese, said Real's "quality" should see them through to next month's final, also in Munich, where they would meet holders Barca or Premier League side Chelsea, who play their first leg in London on Wednesday.
"We believe in our strengths and I am convinced we will get to the final," Ozil, who plays in the German national team with many of the Bayern players, told reporters.
"I am a bit sad about the defeat but I have a positive feeling," the former Werder Bremen player added. "We'll meet again in Munich."
Bayern coach Jupp Heynckes, who led Real to the Champions League title in 1998, will have noted Coentrao's weaknesses and the Portuguese can expect another torrid time in Wednesday's second leg - if he is selected.
