The Turkey international has acknowledged that BVB face a tough task to progress, but refuses to throw in the towel just yet
Goals from Gareth Bale and Isco before the break gifted Madrid a comfortable lead at half-time, before Cristiano Ronaldo piled even more misery on Dortmund after the break.
Nevertheless, Sahin is not giving up just yet and hopes the Bundesliga side can turn things around in the return.
"We are 3-0 down in the tie but we still have a small chance; our coach told us just that after the game," Sahin told uefa.com.
"We missed [Robert] Lewandowski today and we are happy he will be back next week but it will be another tough game nonetheless.
"Last year we won the [semi-final] first leg 4-1 and the second game here was very difficult, we lost 2-0 and almost conceded a third, so we know that anything can happen.
"It was a difficult game for us. We knew that Madrid would bring their quality and speed but we also knew we would have chances, which in the end, we didn't take."
The return at the Signal Iduna Park is scheduled to take place on April 8.