Hertha striker Julian Schieber, who quit Dortmund for Berlin at the end of last season, scored the hosts’ first-half winner which saw them overtake 16th-placed Borussia to go 13th in the table.
Dortmund qualified for the Champions League’s last 16 as group winners ahead of Arsenal, but their dire domestic form this seaso has seen them win just four of their 15 Bundesliga matches.
They are the only team in Germany’s top flight to have lost nine matches having started December bottom of the table.
Despite Saturday’s defeat, Dortmund’s fans applauded the squad after the final whistle at Berlin’s Olympic Stadium and Klopp led his side to their fans’ corner to acknowledge them.
“We need all the support we can get, we hear week after week that we are a great team, but this ‘awesome’ team also has awesome problems,” admitted Klopp.
“The first half was the complete opposite of how we wanted to play.
“We weren’t determined enough which is completely the wrong path to take in a game like this.”
Klopp, who steered Borussia to the 2011 and 2012 Bundesliga titles, has a contract until 2018 and has been told his job is safe, but last season’s runners-up were poor in Berlin.
“We’re in a relegation battle, we’ve accepted the situation the way it is,” admitted Klopp.
Dortmund host second-placed Wolfsburg on Wednesday, then are away to fellow strugglers Werder Bremen next Saturday in the last game of the year before the Bundesliga breaks for the winter.
“We now have two games left to dramatically improve our league position in the second half of the season and that is our task,” said Klopp.
There was more bad news in Berlin as Armenia play-maker Henrikh Mkhitaryan came off after 35 minutes and could be ruled out of their last two games.
“He felt a sharp pain, which is not good when you have three games in a week, and it looks like he won’t play again this year,” said Klopp.