Dortmund are top of Champions League Group D with two wins from their two matches, beating Arsenal 2-0 at home and Belgian champions Anderlecht 3-0 away.
But Klopp's side are enduring a horrible run domestically and Saturday's loss, their first in Cologne since 2003, was their third Bundesliga defeat in a row ahead of their European clash in Istanbul.
"We played a type of football which makes absolutely no sense," fumed Klopp.
"We had a high number of failed passes and committed simple mistakes which really hurt us.
"We have to correct these errors. Not tomorrow, or the day after, but now.
"To concede two goals in each game is rubbish. We have to sort this out and no one will help us do that."
Dortmund's Germany midfielders Ilkay Gundogan – who had been out for more than a year – and Marco Reus returned from injury, but were powerless to stop Cologne taking a 1-0 lead as midfielder Kevin Vogt fired home on 40 minutes.
Italy striker Ciro Immobile equalized, but Cologne's Simon Zoller netted the hosts' winner on 74 minutes.
The result sees Dortmund drop to 14th in the Bundesliga table – just two points above the bottom three – while Cologne are 10th.
Dortmund travel to face league leaders Bayern Munich away in a fortnight and Klopp's side are already 13 points behind the Bavarians after only eight matches.