Injuries in the back line has essentially been the story of the season IMO. MC is giving up goals are roughly 150% of the rate they were last year. I mean it's not horrible but you don't win the league that way. Losing Sane was also a factor; under rated player I think.
Liverpool is on a roll and your point about belief is a good one. And maybe that's the difference. From what I've seen they aren't as potent offensively but they seem a bit more stout defensively. A lot of "bend but don't break" going on.
I'd put a 20 on Leicester. Liverpool are going to drop points sooner or later, Leicester is playing well and Liverpool has a rough December schedule. And I'd add I wouldn't be shocked if MC came in 3rd behind Leicester this season; I like the way they are playing.
I think city is fine long term, it's just a rough season. The team is a bit battered and little jaded/fatigued. You need a little luck to won trophies and this season they aren't getting it. What are you going to do?
Shore up the back line, get healthy and look to next year. If you can go all in on what trophies are still possible come January and see to next year.