The 59-year-old was confirmed as Julian Nagelsmann's successor on Friday, signing a four-year contract that runs through to the 2030 World Cup, which will be co-hosted by Spain, Portugal and Morocco. Nagelsmann stepped down this month in the aftermath of Germany's shock last-32 exit to Paraguay at the World Cup.
Klopp did not hold back when addressing the German press for the first time in his new role.
"If you behave badly and don't leave my family in peace then I'll be gone, I'll just turn away," Klopp said.
"I know there are other countries where national team coaches are treated even worse.
"I'm not doing this job for myself, I'm doing it for you. I'm taking this job even though I've seen how you've treated Julian Nagelsmann and Thomas Tuchel.
"I love this job but I am always ready to call it quits if need be."
Both Nagelsmann and England boss Thomas Tuchel faced heavy scrutiny after their exits from the World Cup, with Tuchel criticised for his tactical set-up and substitutions as England surrendered a 1-0 lead in their semi-final defeat by Argentina before recovering to finish third at the tournament.
It is Klopp's first coaching role since he left Liverpool at the end of the 2023-24 season, having stepped away citing a need to recharge after nine years at Anfield during which he won six major trophies. He said the timing now felt right to return to the touchline, and for his first job in international management.
"Over the last few days it was almost like a movie happening to myself," he said.
"I have always surmised the job of Germany head coach is really big but now it is really dawning on me what being the national team head coach is all about.
"For many, many years it was unimaginable for me to assume this position. As the years went by, it became more or less evident that sooner or later I would be asked to do this job.
"Now I think the time is right."
Klopp added that he considers the Germany post the pinnacle of his coaching career and does not intend to take on another job once his time with the national team comes to an end.
"Jurgen Klopp is not going to have any 'career' after the national team," he said. "This is the pinnacle, the absolutely high point of my footballing career as coach. I will give everything I have got."