A 4-1 defeat to Freiburg yesterday [Saturday] means Cologne remain only two points clear of the automatic relegation places and facing a tall order to beat second-placed Bayern.
However, given the way Hertha Berlin were thrashed 4-0 by Schalke yesterday [Saturday], the chances of them beating Hoffenheim next weekend look equally slim, meaning even defeat could leave Cologne with a play-off against the team which finishes third in the second division.
"Initially, I was frustrated, but then I developed hope," said Schaefer to LIGA total television.
"That is because we are capable of different performances at home.
"The final day of the season always has its own script and the situation is clear - we have to confront Bayern openly."
Cologne's general manager Claus Horstmann is also confident that the Goats will save themselves against the Champions League and DFB-Pokal finalists.
"We have beaten then before," he said. "We have a different face at home and we will accept this challenge and, from today, we will fight for it.
"We have to concentrate all of our efforts on Bayern. We are not praying that we beat them, we are working hard on doing so."