I see two big issues facing us going forward (setting aside the whole question of how long the manager can last at this point).
1)Our work at set pieces is dire, both in defence and attack.
2)Our midfield is so, so static.
Fixing number one I think is doable; after all, we were brilliant at set pieces in 2013-14, and that wasn't all down to Suarez. Gerrard's delivery, while certainly better than Milner's, wasn't world class, but we were still scoring a goal or two every month from set pieces, and we weren't giving those cheap goals away. In my opinion the big difference was patterns of movement in the box, coordinated with the set-piece taker knowing which pattern of movement was going to happen, leading to a decent amount of free headers. Granted, there was a bit of luck involved in how many of them actually went in, but there was a clear plan and one that had been worked out beforehand. Yesterday, our set pieces looked like Milner was just trying to go near post, while the runners in the box weren't sure what his plan was. It was completely dysfunctional. And we were terrible at defending them as well, just all over the map with no coherent plan other than "everyone try to keep the ball out the goal."
Fixing number two is fixable as well, but probably only with another player brought in. I don't want to beat him any more than I already have, but bringing in Milner was a terrible idea. Actually, it wouldn't have been that bad an idea if he had come in to do what he did at City, sort of a utility player who is good enough to bring off the bench in any of about 4 positions, but backup in all of them. The part that makes it a bad idea is that we essentially promised him a starting role in the centre of midfield to get him to come, which is hamstringing Rodgers at the moment.
Put it this way: imagine if we had gotten William Carvalho instead of Milner, and let Lucas leave. Right now we could play a 4-2-3-1 with Can and Carvalho sitting behind 3 of Ibe, Coutinho, Lallana and Firmino. Or a 4-4-2 diamond with Carvalho sitting, Can and Coutinho ahead of him, and Firmino behind Sturridge and Benteke. Either of those two options look very solid, preventing us from being cut apart by a simple pass or two on the counter, but yet setting a firm foundation for us to attack from. And that's without Henderson, who could come back from his injury and very capably fill a number of roles surrounded by those players.
Instead, we have a midfield that looks exactly like what it is - a bunch of above-average players. And you can get away with a number of above-average players, as long as you have a Suarez and a Gerrard or two to come up with about 15 goals a season out of nothing. Getting your first 50 or 55 goals is easy, at the level of spending we're doing. The hard part is finding those players who can turn 55 goals into 70, who can take us from sixth to fourth by virtue of those 8 extra points they earn us when they have no right to score. And a big part of that is a dynamic midfield, with a couple of players who you expect to consistently do things like that every third or fourth game. We simply don't have it right now, and that's why we're nowhere. We have Coutinho, and we hope that Firmino can develop into that kind of player.
If Benteke can at least score the ones he should score, and Sturridge can stay fit, then we'll get 60 points at worst. The question is whether Firmino or Coutinho (or someone else) can somehow change things around enough to get us to 70 or 75 and in with a shot at fourth. And at this point, you'd have to say the smart money is firmly against that happening.