The German side go into the first leg of the last-32 tie on a five-match losing run in the Bundesliga, which has seen them drop to 14th place.
The latest defeat was a 4-1 reverse at home to Werder Bremen, and Niedermeier accepts the team have to win back the disgruntled supporters.
"With five defeats in a row it is clear that some fans will stay at home," the 26-year-old said at a press conference.
"We ourselves are partly to blame for that and have now been challenged to play better so more fans come back."
Stuttgart can still turn their season back around. They are only six points off the top five and nine above the relegation zone.
But opponents Genk are faring rather better in the Belgian Pro League, lying fourth in the standings with two wins from their last two outings.
Genk topped their qualifying group, going through the six games unbeaten, while in their pool Stuttgart just scraped through on head-to-head record with four points fewer.
But Niedermeier says neither that nor domestic form will have any bearing on Thursday's game.
"It is the first of two games," he added. "Neither the group stage nor the losing streak of the Bundesliga has a meaning."
And Stuttgart coach Bruno Labbadia wants to take a lead to Belgium, saying: "Of course we want to build an advantage, because a cauldron-like atmosphere awaits is in Genk."
Niedermeier will be tasked with keeping an eye on Belgium striker Jelle Vossen, the 23-year-old who has scored 16 goals in 23 league games this season.
"He stands out and it is great to be able to go up against such a player," the German said.
Stuttgart could be without midfielder Christian Gentner, who is struggling with a shine problem, while Daniel Didavi is definitely out.