Jurgen Klopp could not believe Scott Parker was sacked by Bournemouth after losing 9-0 to his Liverpool side, suggesting "the right owners" would not have made such a decision.
Saturday's game at Anfield tied the record for the biggest defeat in Premier League history, with Bournemouth completely outclassed.
It was a third defeat in a row for the newly promoted outfit, who had also been comfortably beaten by Manchester City and Arsenal without scoring.
A Bournemouth statement confirming Parker's departure on Tuesday appeared to suggest his dismissal was not based on results alone, as it stated the head coach had to be "aligned in our strategy to run the club sustainably".
"We must also show belief in and respect for one another," it added.
Parker had bemoaned Bournemouth's lack of transfer activity since their promotion from the Championship and even suggested the Liverpool loss had not come as a surprise and could be repeated without action in the market.
Regardless, Klopp felt this call was "really harsh", referring to it as "unbelievable" as a question on Parker was posed to him at a news conference later on Tuesday.
"When I heard it today, that's the moment where you realise how important the right owners are," he said.
"We all know there are different systems in the Premier League, how clubs are led.
"Some rules don't allow them to do exactly what they want. If they could stretch their resources, that would be strange – they could do anything, because they are owned by countries.
"Then other clubs who have other structures, like us or Arsenal or whoever, and then there are clubs like Bournemouth. You saw three teams coming up, Fulham, Nottingham Forest and Bournemouth.
"Nottingham is spending like... they spend. Fulham is doing some stuff. And I can't remember that Bournemouth did a lot.
"That is obviously difficult, if you come up from the Championship and arrive in the Premier League. That is not easy, so I felt for Scott.
"It's not that his team are not good enough, not at all. I'm not sure where you get that idea if the first four games gives you Arsenal, City and Liverpool.
"If you have nervous owners, that's like set up for a new manager: 'Let's see how he can do.'
"That's why I was very surprised, very surprised. I think Scott is an outstanding manager, to be honest – what he did with Fulham, in his first job, and now Bournemouth, in the Championship, getting up.
"This is an outstanding achievement and really difficult, and then you get four games and three of them are Arsenal, City and Liverpool, and your owner tells you, 'see you later'. That's really harsh."
That does not mean Klopp and Liverpool are always on the same page, as he explained there were also sometimes disagreements about the Anfield club's approach, even if he is now accustomed to how they work.
Asked if he had been backed, Klopp replied: "This summer? What does it mean, 'backed'?
"What I don't like is that if I say 'I'm not sure', we make a massive thing of it, but I realised as well it was always like this. Was it always easy? No."
He added: "Let me say it like this: from time to time, I would like to risk a bit more, but I don't decide that. We have a great team, and we will really try to squeeze everything out of this season."