Dortmund fell to a comprehensive 3-0 defeat to Real in Wednesday's UEFA Champions League quarter-final first leg at the Bernabeu, with Gareth Bale and Isco firing Real Madrid into a 2-0 half-time lead before Cristiano Ronaldo netted for Carlo Ancelotti's men after the break.
Jurgen Klopp's charges had chances of their own as the likes of Pierre-Emerick Aubameyang and Henrikh Mkhitaryan went close, yet Dortmund failed to find a crucial away goal.
The result means Dortmund - who knocked Real out of the Champions League at the semi-final stages last season - face an uphill task in the second leg at Signal Iduna Park on Tuesday.
Sahin is refusing to give up hope of an unlikely comeback, but conceded Dortmund's chances of progressing are slim.
"We were not without chances, but we need to play smarter," he told Dortmund's official website. "We created a lot of counter-attacks, and should have taken at least one of them.
"And so we ended up without a goal, which makes our task in second leg a very difficult one. Their goals, of course, were also a testament of Real Madrid's quality.
"In addition, things didn't go our way from the start when they scored that early goal. Everything is possible in the second leg, but of course we have to be realistic."
Forward Marco Reus believes Dortmund were made to pay for a poor first-half performance.
"If we had played the first half the way we did in parts of the second, we could have gotten a better result," he commented.
"Now we have to accept this result, which of course is not a good one for the second leg."
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