Klinsmann stepped down after 11 weeks in charge of Hertha and three wins from nine league matches, citing a lack of "trust" from the club's hierarchy.
In a Facebook Live video on Wednesday, the former Bayern Munich, Tottenham and Germany striker expanded on this – alluding to interference from above and disagreements on "many things".
When he resigned, Klinsmann said he expected to resume a role on Hertha's supervisory board, but primary investor Lars Windhorst told a news conference on Thursday that his conduct had made this an untenable prospect.
🗣️ #Gegenbauer:— Hertha Berlin (@HerthaBSC_EN) February 13, 2020
"Of course he signed a contract for employment, both written and verbally. Mr. Klinsmann confirmed the suspension of his position on the supervisory board of the KG on 27th November, before signing as head coach on 1st December." #hahohe pic.twitter.com/H7K5O88x8N
"Unfortunately, I must say that the way Jurgen Klinsmann resigned makes a further working relationship with him on the board of Hertha BSC impossible," Windhorst said.
"Unfortunately, the way he left is so unacceptable that we cannot continue a constructive collaboration between him and the other people in charge.
"If we can count on him and his guidance in some other form in the future after all the dust has settled, we will see. I am neither shutting any doors, nor am I knocking anyone out as it has been written today.
"However, it is regrettable that his resignation has been so abrupt, which is why Jurgen Klinsmann lost a lot of credibility. That is really sad."
Hertha's sporting executive Michael Preetz conceded there were differences of opinion between himself and Klinsmann, although he felt the latter might have exaggerated these for his own ends.
"There are different views [between Klinsmann and me] on how the job of a head coach is defined," Preetz said.
"It is correct that we could not agree until he resigned. However, things that I heard yesterday, that I am sitting on the bench and show up on the sideline, were never discussed between the two of us.
"If there are problems and conflicts then I am used to discussing them and to try and find a solution. You can't do that if you turn around and run away."
A 3-1 defeat at home to Mainz in what proved to be Klinsmann's final game at the helm left Hertha 14th in the Bundesliga – six points ahead of third-bottom Fortuna Dusseldorf.