The Germans were outplayed in front of their own fans on Wednesday, as Real's attacking superstars came to the fore to all but seal the Spaniards' place in the quarter-finals.
Once Carlo Ancelotti's side had opened the scoring through Karim Benzema in the 13th minute, only one team looked like leaving the Veltins Arena with their hopes of progression intact after the first leg.
Benzema, Gareth Bale and Cristiano Ronaldo all netted twice, before Klaas-Jan Huntelaar registered what will more than likely prove to be scant consolation for Schalke in injury time.
Ancelotti's side wasted a host of other chances in the first half that could have made the scoreline even more one-sided, and Draxler acknowledged that the Liga side were simply too good.
"The difference in quality was clearly noticeable," he said. "We have to thank our fans for the great support they gave us throughout.
"We made several mistakes and Real Madrid punished us clinically.
"We tried to adjust and keep going forward, but you simply don't have a chance against a quality side like Real Madrid if you make the type of mistakes that we made today."
Schalke coach Jens Keller reinforced Draxler's view that the hosts had made too many mistakes, and he rued a crucial miss from the winger just after Benzema's first goal, as Iker Casillas made a brilliant save to deny him an equaliser.
He said: "A mistake allowed Real to score the opener but we immediately had the chance for the equaliser.
"These types of chances don’t come along that often against a side like Real.
"We are a young team that still has lots to learn at this level. We made too many simple mistakes tonight. We had a good start to the game, played up the pitch bravely until we conceded the opener."
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