Werder went down 1-0 at Bayer Leverkusen, sunk by a controversial penalty converted by Stefan Kiessling in the 35th minute, and are just two points above Augsburg who occupy the relegation playoff spot with three matches to play.
The four-times champions and seven-times runners-up have collected four points in 10 games since a 4-1 win over VfB Stuttgart, a run that included a 6-1 defeat at Bayern Munich.
Despite the dire situation, general manager Thomas Eichin was quick to stamp out media speculation that coach Thomas Schaaf's 14-year reign was about to end.
"A coaching change at this point would be absolute nonsense," Eichin told German media. "We are not discussing it."
The defeat came one day after Werder suspended Austria forward Marko Arnautovic and Dutch midfielder Eljero Elia after the pair were caught speeding on a motorway early on Friday morning.
Arnautovic, who was involved in several disciplinary problems for club and country before joining Werder in 2010, and Elia have been banned from training.
Schaaf was pleased with his team's commitment and discipline on Saturday but said they lacked conviction in attack.
"I have to admit we were not so convincing going forward, our moves broke down early and we lost the ball too easily," he told a news conference.
"Maybe because of the situation in which we find ourselves we wasted some chances we might have taken in other circumstances.
"Nobody can reproach the players today. We take a lot of positive things from this game and still believe in ourselves. But we need to start winning matches and collecting points."
Werder, who followed their 2004 title with four successive top half finishes, have spent only the 1980-81 season outside the top flight since the Bundesliga was founded in 1963.