Roy Hodgson paid the price for the way he talked, not just results. And the truth is he overdid it - his uber-humble tone sounded really weak and was just embarrassing for a big club.
Nevertheless, there was an underlying wisdom to what he was trying to do. Liverpool's problems, IMO, stem in part from mismanagement at board level but in part from their fans. The ridiculous, unrealistic expectation levels are just corroding their club. It ruins good players, makes decent sides perform badly.
Hogson rightly decided the first thing he needed to do was calm them the feck down, get them to lower their expectations and build slowly back to winning ways. He played it badly as I said, but you can see what happens when they go the opposite way - get a manager in who is basically one of their mental fans, with all the delusions of grandeur, bitterness and constantly injured pride that goes along with it.