Real Madrid's Cristiano Ronaldo (R) heads the ball to score his second goal past Schalke 04's goalkeeper Timon Wellenreuther during their round of 16 second leg soccer match at the Santiago Bernabeu stadium, in Madrid, March 10, 2015. [Photo/Agencies]

MADRID - Holders Real Madrid survived a huge scare when they lost 4-3 to Schalke 04 in the Champions League on Tuesday but squeezed into the quarter-finals 5-4 on aggregate thanks to record European marksman Cristiano Ronaldo.

Coming hard on the heels of a 1-0 defeat at Athletic Bilbao in La Liga last weekend, the loss to a battling Schalke side did nothing to dispel the impression Real have lost their way and they were whistled off the Bernabeu pitch by their angry fans.

Two first-half goals from Ronaldo, which took his tally in European competition to a record 78 goals, and a Karim Benzema strike just after the break saw Real reach the last eight but Schalke came close to pulling off a remarkable comeback.

Striker Klaas-Jan Huntelaar scored twice for the visitors, including a superb late winner on the night, after Christian Fuchs has put the German side in front after 20 minutes, with substitute Leroy Sane also on target for the Bundesliga side.

It was Real's first Champions League defeat at home in 22 games since Barcelona beat them 2-0 in April 2011 and was only the second time the world's richest club by income had conceded four goals in a European game at the Bernabeu.

"We didn't play well but sometimes you have to suffer," Real midfielder Luka Modric, returning to action as a second-half substitute after a long-term injury absence, said in an interview with Spanish television.

"We have to play as a team and hopefully we will get back to playing the way we did at the start of the season," added the Croatia international, who had been sidelined since November.

"We have the quality and I think we will see the best version of Real Madrid in the next match."