The Turks were comfortably beaten at the Santiago Bernabeu on Wednesday night as Madrid made a significant step towards reaching the semi-finals of the competition.
"Despite all our work and training, we did not expect to concede such goals," Terim is quoted as saying by Sky Sports News.
"You need to minimise mistakes in such games. Real Madrid were the dominant side and I accept that."
Galatasaray welcome Madrid to Istanbul for the second leg on Tuesday.