The Bundesliga side exited the Champions League on Wednesday after a lopsided aggregate defeat.
Tim Hoogland said he was proud of the character shown by Schalke in its Champions League defeat to Real Madrid.
Real wrapped up a 9-2 aggregate triumph Tuesday following a 3-1 win in Madrid, though the damage had already been done in the first leg of the last-16 tie when Carlo Ancelotti's men romped to a 6-1 victory.
Hoogland canceled out Cristiano Ronaldo's opener in the second leg at the Bernabeu, but two further goals in as many minutes from Ronaldo and Alvaro Morata put added gloss on an already one-sided scoreline.
Despite the heavy defeat, Hoogland insisted that he and his teammates bow out of the competition with their pride intact.
"We wanted to exit the competition with our heads held high and I think we managed that," he told reporters. "Our first-half performance was good and we even created several chances to score. The Champions League chapter is over for us this season, but we have nothing to be ashamed of. Ronaldo and (Gareth) Bale are world-class players. It was a great experience to play against them."