Dortmund's dismal start to the Bundesliga season continued when they suffered a 1-0 home defeat against Hannover on Saturday.
Klopp's side are fourth-bottom of the table after losing six of their first nine league matches and the charismatic coach could do with a timely tonic when they travel to Bundesliga 2 side St Pauli for a second-round tie.
The 47-year-old called on his players to respond to their latest setback as they attempt to progress.
"The fear of not winning is certainly there," Klopp told reporters on Monday. "Sometimes we lack the necessary rest to perform.
"But we have to work. The preparation has been normal despite the critical situation that we've found ourselves in.
"We know the nature of this competition, that we're out if we lose. A couple of the players are over-worked, but there are no new injuries."
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