The BVB almost let a two-goal lead slip in their Bundesliga clash in Cologne, despite the home side playing the entire second half with a man down, much to the ire of manager Niko Kovac.
"We won a game tonight in which we didn't play well â- as a coach you are allowed to be annoyed about that," said Kovac to SkySports after the match.
"We lost against Bayern last week, but I still liked the way we played. Today we won, but I didn't like the way we played at all. We weren't sharp enough.
"If everyone runs one metre less, then you're missing tackles somewhere, you're missing challenges, and ultimately youâre missing what you need to stay in the game."
The result sees the Croatian mentors side remain in second place, 11 points behind rivals Bayern Munich on the league table, with nine matches left in the season following their UEFA Champions League exit against Atalanta last week.
Dortmund will have full focus on the Bundesliga following their disappointing UEFA Champions League exit against Atalanta last week and will have to hope the Bavarians miraculously implode in order to stand a chance to win the title.