Sahin, who has been sidelined since his signing from Borussia Dortmund by a knee injury, made his competitive debut for Real on the day.
Mourinho welcomed Sahin's long-awaited bow and said: "It was the perfect match for Sahin.
"There was no physical or psychological pressure. He had a long time out and it was a good test today. He now has 15 days (during the international break) to continue improving his form."