What is going/has gone wrong?
1) We didn't replace the fulcrum of our attack with a player who offered similar qualities (skilful with the ball, goal threat, works hard off the ball & closing down). I know there's not another Luis out there, but we needed to replace him with as little disruption to our general gameplan as possible. When we failed to get Sanchez, we just seemed to give up this type of player. I don't profess to have the wide knowledge of European players that many on here certainly do, but there were names touted that made a lot of sense. Yet we ended up signing a player notorious for being a bit lethargic, not much of a team player, and prone to sulks.
2) Rodgers has been too rigid in his tactics. Whilst sticking to one's beliefs can be admirable, there's a fine line until that becomes counter-productive. To some extent, his hands have been tied by injury (primarily to Sturridge), and he's tried to give players like Lovren the time to build a partnership and recapture some of the form he showed to Soton last season. But in other instances he's shown almost a pig-headed refusal to rectify what almost everyone else can see is not working. Ballotelli has looked dog-poor up front alone, but better when partnered with another striker (including the industrious Borini), yet he's persisted in playing Balotelli up front alone in the league. Opponents seemed to figure out Gerrard's shortcomings in the 'quarterback' role; Rodgers persisted with this tactic. We've seen Henderson's form deteriorate, but he's still been picked week in week out. Overall, the team is performing poorly & looking increasingly lacking in confidence; but the overall shape of the team (and I acknowledge certain parts have been adjusted) has remained stubbornly samey.
How do we remedy?
We need to bring in a tricky, quick, hardworking striker in January. I'd hoped at one point we could bring Reus in, but that's delusional with some of the mega-paying/plastic clubs after him (and why would he come to a team struggling for form & results, in real danger of missing out on ECL football next year?). We're going to have to be imaginative - and indeed more generous than we'd need to be if we were sitting comfortably in the top 4 right now.
And Rodgers needs to accept to himself that he's not the messiah/a football genius, and learn to be humble enough to know, when necessary, when he's not got it right, and make changes to his tactics accordingly.