Cologne will not demand that their 5-0 defeat at Borussia Dortmund is replayed, the Bundesliga club announced on Tuesday.
The club did, however, reiterate their stance that Dortmund were incorrectly awarded a goal by the VAR review system and urged the German FA (DFB) to offer clarity on the issue.
Sokratis Papastathopoulos put the ball past Cologne keeper Timo Horn in injury time of the first half, but referee Patrick Ittrich initially disallowed the goal for an apparent foul.
The decision was overruled by VAR, and gave Dortmund a 2-0 half-time lead. But Sokratis' goal was a major discussion point following the match after footage showed Ittrich had whistled before the ball crossed the line and, according to the VAR regulations, a goal could not be awarded as the ball had not gone into the goal before the referee halted play.
"From FC Cologne's point of view the defeat at Dortmund also came about through a clearly irregular goal, at 2-0," the Bundesliga side said in a statement on their website.
While maintaining the club believed a breach of technical rules by the officials would allow for an appeal, Cologne "after carefully weighing up all factors" opted against it. "The reason being that the chances for success of such a protest are slim," the statement read.
Cologne said they would send a letter to the DFB demanding the association "provide legal certainty for the points of contention in the sense of all of the league."
The club added: "The project VAR, which Cologne has always supported, would be foredoomed to failure if the conditions agreed on and communicated before the season are not kept."
Cologne sporting director Jorg Schmadtke on Sunday had announced his intention to protest against the result of the match.