Real Madrid coach Carlo Ancelotti has apologised for his team's performance against Schalke, admitting they deserve all the criticism they get.
The defending champions were booed off at the Bernabeu after losing the second leg 4-3 - despite reaching the quarter-finals 5-4 on aggregate.
Fans also waved white handkerchiefs - a symbol of disgust at a bad performance.
"I'm very sorry. We played very badly and that is bad for our image," said Ancelotti.
"We're professionals, we don't make ourselves look ridiculous."
The 10-time European champions have qualified for their fifth successive Champions League quarter-final but were left hanging on at the Bernabeu as they suffered a fifth defeat of 2015.
Schalke, who were trailing 2-0 from the first leg, applied heavy pressure late on for the one goal they needed to qualify as Real lost for the first time in 22 home Champions League matches.
Ancelotti ended his first season in charge by winning the Champions League last May, but has faced growing criticism from sections of the club's support this time round.
|Real's home dominance|
|The only two teams to beat Real Madrid at the Bernabeu by two goals in the last 10 years of the Champions League are Juventus in November 2008 and Barcelona in April 2011.|
"All the criticism we get is justified," Ancelotti said. "We need to look at our defence, that's where all our errors were. No team has put four past us at home.
"We had problems in every aspect of the game: offensive; defensive; desire; fight and concentration.
"It's not easy to explain what's happened. We've lost confidence. It is quite incomprehensible after what we did until December," said Ancelotti, whose players including Gareth Bale appeared dejected at the final whistle.
Schalke threatened to become only the third team to win by two goals at Real in the last 10 years of Champions League football, taking the lead on the night on two occasions through first-half goals from Christian Fuchs and former Real striker Klaas-Jan Huntelaar.
Ronaldo twice pulled Ancelotti's side level with headers before half-time, and Karim Benzema put the hosts in front early in the second half.
But Schalke earned a fully deserved win thanks to further strikes from Leroy Sane and Huntelaar.
Schalke boss Roberto Di Matteo, who won the competition with Chelsea in 2012, said: "We have mixed feelings.
"The team showed a really high level. We tried everything to stay in the competition. Tonight we won the match, but nevertheless it wasn't enough."