Sahin, who has been sidelined since his signing from Borussia Dortmund by a knee injury, made his competitive debut for Real in their 7-1 win.
"It's been a great day for me. I wish to thank everyone at the Santiago Bernabeu, my teammates, the manager and the President. I must now work hard to be able to help the team," said Sahin.
"I'm very happy for playing my first game with Real Madrid. It's been difficult being injured. I was a little nervous before coming on because it was my first match before the fans. I felt confident and happy after a couple of minutes. We must continue to work hard because we will face difficult games after the league break."