It was their third straight Bundesliga home defeat and a fourth reverse in six league matches.
"We can really use this break now but it is only our fault," Klopp told reporters. "Something that started well has ended badly."
Dortmund fans continued to show their backing after Saturday's game, unfurling banners of support and thanking the players for a great year.
The Bundesliga crown looks out of reach for Klopp's third-placed team at the halfway point of the season, 12 points adrift of Bayern Munich with the leaders also having a game in hand.
"This is hard and it will take some time to process," said the coach.
Dortmund also had to wait nervously until the last group match to advance to the last 16 in the Champions League where they will meet Zenit St Petersburg over two legs in February and March.
"I can say a lot of things in support of the team but we should have lost none of the games that we lost this season," said Klopp.
Hit by a seemingly endless string of injuries that severely reduced his options, especially in defence, Klopp has seldom had the luxury of choice.
The Dortmund coach has been forced to bring in a number of youngsters this season to compensate for losing players like Mats Hummels, Neven Subotic and Ilkay Guendogan.
Two youngsters, Erik Durm and Marian Sarr, lost possession of the ball to gift Hertha pair Adrian Ramos and Sami Allagui their first-half goals after Marco Reus had put the home team in front after seven minutes.
"The way we reacted after the second goal was clearly not good, that much I can say," said Klopp. "We let Hertha back into the game completely unnecessarily."