The Turkey international scored twice for the defending champions, as they registered a 5-1 home win in the Bundesliga.
"The coach [Jurgen Klopp] had said it time and time again, it was only a matter of time," he told ARD.
"I'm not hiding my bad passes, but that's part of my game and the coach knows that. I had not performed well against Hamburg, but today was put in charge of making things happen again and succeeded.
"I was a bit frustrated in the first half, but in the end it was another important step in our development."
Sahin joined Dortmund on loan from Real Madrid in January for until the summer.