After Robert Lewandowski scored twice in Bayern's 4-0 thrashing of Union Berlin on Saturday, second-placed Dortmund lost ground in the title race with seven games left.
"It was intense, there was a lot of back and forth," Dortmund centre-back Manuel Akanji told DAZN.
"We had a lot of chances, but in the end, we just didn't score. That's not enough."
Haaland cut a frustrated figure as he returned to the starting line-up for the first time since January following injury, and has now failed to score in his last three appearances.
Two of those have come as a substitute, but it is the longest the 21-year-old Norwegian has gone without a goal since joining Dortmund in January 2020.
Dortmund took the lead after just eight minutes when Marius Wolf snapped up a Jude Bellingham pass and scored his second goal in as many games.
Koln were level by halftime after Anthony Modeste's flick was tapped in at the far past by his forward partner Sebastian Andersson.
Dortmund showed few ideas of how to break down the resilient Cologne defence in the second half.
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