Yes, you are actually right, finishing in the top four will be difficult if they continue losing games like this because if other teams around them keeps on winning games and they are not winning, it would be very difficult for them to claw their way back into the top four considering the fact that they aren't that good like before that they can win ten games straight, so in as much as they are not in their best form now, they really have to stay close to the top four, so that they can sneak into the top four at the very end or they can secure a place in the top four convincingly, because it would actually be a disaster for the citizens not to qualify for the uefa champions league, they really need to, so that it would be easy for them to sign top quality players in the summer transfer window.
Then as for their performance yesterday, truly they were terrible at the back, and Liverpool would have scored more if they were more clinical in front of goal, because honestly speaking, i expected Liverpool to score more, but it wasn't meant to be, the most important thing was to secure the three point which they did, and the most important thing that buttress this winning was arsenal losing to westham united.
As it stands like this I don't know what to think again about Manchester City, city is not what they use to be again, so I won't be surprised if they don't finish in the top four, this things aren't magic rather it is about showing working, city messed up yesterday by allowing such goals from Liverpool, though I already know that Liverpool was going to win them, I have evaluated their performance early this season and now, I was able to come to the conclusion that there is no way they could battle with Liverpool this period without being defeated and that was actually what happened in both teams meeting, if we have to put there performance into consideration then we wouldn't be expecting anything from Manchester City this season, for me I think there's absolutely nothing they can do again this season, it will be for them to get very much prepared for next season as for this season, I think it is over for them.
Manchester City defense has been unlike them and that's the problem they have been encountering recently, yea I agree with you that Liverpool would score more if they had utilized their chances, just as you said what Liverpool needed is to bag the 3 points and they actualized it, so is it.