I honestly think it's all a bit of an exaggeration, yes Liverpool were overall better than you, but let's be real here, it was hardly complete & utter domination with attack after attack looking like it was going to be 5 or 6, you definitely didn't get raped the way United did in the first half against City, in fact the Pool rarely created clear-cut chances, which I was surprised about considering how fluent they've been this season. A defensive embarrassment from a set-piece and a wonder strike was the only thing that broke your lot down, dare I say Chelsea possibly had more or at least equal clear-cut chances (the one the springs to mind was a Costa chance to make it 2-2, but hit it straight at the keeper). You exposed their defensive frailty when you got the goal, and controlled the game from there on, but you'd have to be disappointed not to have tested their back four more after that, not getting Hazard more on the ball more, and I do agree the substitutes were introduced a good 10 minutes too late.
Liverpool deserved the win, a fantastic result for them, but I don't think this requires any panic or undoes any of the progress that Conte has made so far. Relax, I also think an away trip to the Emirates is the perfect fixture to follow this, if you stand up to be counted & get a result, it's the perfect morale booster.