For me, the big difference yesterday was that we didn't give the game away. Against Norwich and Southampton, we lost the games instead of making them beat us. Swansea worked some openings, but weren't handed anything gilt edged. If you give away the first goal, the whole game changes.
Man City are comfortably good enough to beat us, as are Liverpool, but we have to make them do it. By the sounds, Everton rested players to go all out in the Merseyside Derby, so it may push Klopp into trying harder than he would have done otherwise in that game. Europa League has to be their biggest priority, so we might get an relatively easy ride at Anfield. Again though, we have to play error-free.