Stuttgart stay loyal to struggling Babbel
It was Stuttgart's third league defeat in a row.
"There is no discussion about the coach," Stuttgart sports director Horst Heldt told reporters. "Markus will be sitting on the bench on Tuesday."
Former Bayern Munich and Liverpool defender Babbel, in his first full season in charge while studying for his coaching licence, took over last year and steered them to a third-place finish and Champions League spot.
But this season, with top striker Mario Gomez joining Bayern, Stuttgart have been disappointing, collecting only eight points from 10 games.
They are also third in their Champions League group with two points from three matches after a 3-1 home defeat by Sevilla on Tuesday.