The Turkey international was bitterly frustrated by the way in which Jurgen Klopp's men threw away an early advantage in Saturday's 2-1 loss to Hertha Berlin at Signal Iduna Park
Die Schwarzgelben were beaten 2-1 by Hertha Berlin at Signal Iduna Park on Saturday, meaning they go into the winter break 12 points in fourth place, 12 points behind their Bavarian rivals, who also have a game in hand.
Sahin was particularly frustrated by the loss as Jurgen Klopp's men had actually gone in front through Marco Reus seven minutes in, only to succumb to goals from Adrian Ramos and Sami Allagui.
"We should have added to our lead after going in front, but we took our foot off the gas," the Turkey international told Bundesliga.com.
"We need more of a killer instinct to win these types of matches. Had we scored the second goal, Hertha wouldn't have got back into the match.
"They defended well in the second half and took advantage of our errors in the first. We're very frustrated."
Sebastian Kehl echoed his team-mate's sentiments, admitting that last season's Champions League runners-up had effectively switched off after Reus' opener.
"We stopped playing football after making a good start to the match," the 33-year-old lamented.
"We let Hertha back into the game with those two goals and we couldn't break them down in the second half.
"The defeat is very, very disappointing - it's our third home defeat in a row and we're going to have to wait until the start of next year to put things right."
Dortmund will resume their Bundesliga campaign against Augsburg at Signal Iduna Park on January 25.