Jurgen Klopp's side have failed to match the heights of recent campaigns and sit 17th after losing 10 of their 17 league matches.
However, Dortmund's European exploits have been far more impressive, with a last 16 tie against Juventus secured after winning Group D.
Chief executive Watzke knows top-flight survival is the priority, but does not feel their Champions League aims have to suffer as a result.
"The focus should clearly be on the Bundesliga now, [but] we do not write off the Champions League," he told Bild.
"It might make it a lot easier if we were not in the Champions League and we only needed to focus on the Bundesliga.
"But that would not only be grossly unfair to the competition, but a disaster for German football.
"We have a responsibility to German football."
Dortmund have been in the Bundesliga since 1976, and have finished in the top two in the last fours years – winning it in 2010-11 and 2011-12.
