Ronaldo converted a spot kick during the 90 minutes but Bayern keeper Manfred Neuer saved his later effort
The Spanish capital was in shock on Thursday after Real Madrid joined arch rivals Barcelona in being knocked out of the Champions League as a result of their failure to score from the penalty spot.
"We were stunned" said the front page of Madrid-based sports daily AS below a photo of the Real Madrid players watching Cristiano Ronaldo's penalty in a nerve-jangling shoot-out against Bayern Munich being stopped.
"So close and yet so far!" blared the biggest-selling sports paper Marca alongside a photo of downcast Real Madrid coach Jose Mourinho on his knees by the field.
Bayern goalkeeper Manuel Neuer emerged the hero as his side went through to the Champions League final after beating Real Madrid 3-1 in the penalty shoot-out at the Santiago Bernabeu stadium.
The tie went to penalties after Bayern lost 2-1 after extra time, having won by the same margin in the first leg.
But Ronaldo and Kaka both failed to beat the 'keeper from the penalty spot, and Sergio Ramos then smashed one over the bar.
As a result, Bayern go through to face Chelsea in their own Allianz Arena in Munich on May 19.
Several papers said Real's penalty failures echoed Barcelona star Lionel Messi's crucial penalty miss against Chelsea the previous night which helped to seal Barcelona's exit.
"Cristiano, Kaka and Ramos followed Messi's path," lamented AS.
But AS's front page also highlighted Mourinho's clearest indication yet that he will stay with Real Madrid despite longstanding rumours that he was fielding invitations to join English clubs.
"My feeling is that I will stay on," the Portuguese coach told reporters after the match.
Marca criticised Madrid's performance.
"Farewell to Munich, an untidy Madrid squandered an historic chance to dispute the Champions League final," said its front page.
Real Madrid have been European champions nine times and were hoping to make it 10.
Barcelona-based newspapers showed little sympathy.
"Very tough KO at the Bernabeu at the hands of Bayern who were far superior," said major Catalan daily Sport, splashing a photo of Ronaldo with his head in his hands.
"Out!" cried the front page of Barcelona-based Mundo Deportivo.
Both Catalan papers said Barcelona had a "Plan B" in case coach Pep Guardiola decides to leave.
Sport, without naming sources, said three candidates to replace him included France coach Laurent Blanc, Olympiakos coach Ernesto Valverde and Athletic Bilbao's Argentine coach Marcelo Bielsa.
Mundo Deportivo, also without naming sources, said England were trying to lure Guardiola to succeed Fabio Capello and lead the national side to the 2014 World Cup.