The loss was Bremen's third in a row and left them seven points above the relegation zone in 14th.
"It is not up to me to decide," Schaaf told reporters when asked whether he could be sacked.
"We have officials in this club who in the end have to judge me. I try to do my job."
However, Bremen's general manager Thomas Eichin has said that the club have no plan to fire Schaaf.
"We have to show what we can do on the pitch and not during the week," he said. "Thomas Schaaf will work on this."
Schaaf has been the Bremen coach since 1999.