Jurgen Klopp's men enjoyed a comfortable 3-0 win at Wilhelmshaven in the first round of the DFB-Pokal on Saturday thanks to goals from Kevin Grosskreutz, Marvin Ducksch and Robert Lewandowski.
Sahin played the full 90 minutes but, despite the win, he admits there is still work for the team to do.
"We moved the ball around pretty well," he told the official Bundesliga website.
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Sahin, on loan from Real Madrid, believes his team-mates can kick off their campaign in positive fashion at the SGL Arena as they look to challenge champions Bayern Munich for the Bundesliga title.
"We've got a few days to go till it kicks off, but from here on we're settling into the normal Bundesliga rhythm," Sahin continued.
"The win at Wilhelmshaven was a successful start, which is all that matters."
Augsburg, who also won their DFB-Pokal first-round tie, are more likely to be involved in a scrap at the bottom end of the table rather than the top, having avoided the relegation play-off by just two points last season.
Despite the signing of Halil Altintop from Trabzonspor in the close-season, sporting director Stefan Reuter believes the club's only priority is to stay in the league.
"All we're thinking about is avoiding relegation," he confessed recently.
Dortmund did the double over Markus Weinzierl's side last season, winning 3-1 away and 4-2 at home.