To hopefully fall somewhere between you and @Raziel....
Up to a point I can empathise with Conte.
When you believe you have a winning mentality, winning tactics, winning system, winning culture and that's been rubber stamped by actual 'winning' you're level of belief in yourself is so high that when it's not working your automatic reaction is it must be other people are failing you. Combine this with the thought that you are more than likely doing 70-80 hour weeks, ie working your arse off, frustration will build and if you're a combustible chap, these moments will occur.
The two problems I have is.
1. He didn't say this to the players in the dressing room first (in fact I don't think he said it to them at all). He chose the 'pain in the arse the rest of the time' media to convey his message. Yes, give them a story let them lap it up. Generous to them, disloyal to his club.
2. It was only partly honest. Absolutely zero self reflection, self awareness. All blame arrows pointed away from Antonio. As I said, he's like that because he can't possibly think anything he was doing was causing the situation. In this case I put very little blame on the layers above him. I think they did their best to mitigate the potential issues you may expect with AC. So much so Conte has barely muttered a grievance beyond 'Club signing'.
The sad truth for him is he is provided with the very best of everything to facilitate his training/coaching regime, and undoubtedly he puts the hours in. He lives and breathes football. Unfortunately that actually counts against him if things aren't working, everything is on his watch. He is (was) the captain of the ship.
So things are often "somewhere in the middle"
That said, point 2 is the main problem. Do the owners and players deserve blame? yes, absolutely. Does Conte? yes, as much if not more.
And as a future club hiring, I'd be very skeptical of Conte at this point, none of us can improve if we fail to acknowledge or even see our own failures/challenges. If after 18 months you don't see that your message didn't resonate, didn't get through to the players, that's a problem. I'd also say, he quit (something I defended him for in the past), he gave up, he knew exactly what he was doing in that press conference, and it's a poor play.