How certain are you that it wasn't his fault, or the player's fault? What we know, for certain, is that Jose Mourinho knows more than you or I do. Since the minute the game kicked off, it was evident that Mourinho sent his boys out to suffocate a wounded pig, it seemed very personal.
Probably not the best thing to do for public perception, but I'd sooner stand by a mate than be fake if it was me. Rumour has it they won't be replacing Karanka this season, which imo tells us that there was some personal issues going on, player power or whatever. Just trying to read between the lines.
All we 'know', from The Press is that there was a falling out with Stewart Downing. Downing you will recall dropped into the Ch/Shp when he could have continued in The Prem, just to finish his playing days with his boyhood team. Naturally he is something of a hero to The Smoggies. We also know that Steve Gibson, their Chairman shares the title of The Best Chairman in The Prem, with Bill Kenwright. Steve has never gone for the kneejerk reaction approach to sacking Managers, in the past. He has always backed them as far as he can.
Your opinion of him being the best chairman is also subjective. I do believe he's done a very good job of making a small club punch well above their weight on more than one occasion, but compared to somebody like Levy, he's just a local trader.