When it comes down to it, our 'philosophy' hasn't changed all that much under Jürgen. The focus is still on attack, and on strengthening attacking player options, the FBs getting forward, no traditional holding midfield player.
Rodgers did it, and nearly won the league, but he had better attacking options, and SG.
There's a lot of media about gegenpress, but this season saw some stats to say we're down the stats charts in that area compared with last season (closing, sprints, that kinda sh*te..). We pressed and closed under BR too, just didn't have a fancy German label.
It's just now our defending is more under the scope cause goals have dried up somewhat and goals conceded have more cost.
We've had the same problems defending for years now, and 2 years into Jurgens reign and we haven't much improved the quality of players back there, how the back 4 setup, keeper not commanding, and generally not defending well as a team from set pieces (it's not just the fault of CBs when we concede from free-kicks/corners).
We don't have the balance right. If we're scoring more than we concede, hides it. But it's there, and has been there for years.
Top striker, top keeper would be my first buys. But regardless of new signings, we could surely coach ourselves to be better at defending, though would be at expense of goals down the other end (unless one of the strikers we have hits a clinical streak)
Gareth Barry, Claude Makelele, Darren Fletcher, Gilberto Silva, Javier Mascherano, Dietmar Hamann, N'golo Kante. Off the bat, these are the last pure defensive midfielders that City, Chelsea, Arsenal and Liverpool have used in prior years......and even when Manchester United were playing Scholes and Keane, they did not have a pure defensive midfielder. So it is not something that is a necessity for a top team to compete as long as the players understand the tactical setup employed. Bayern Munich went on to win the Champions League with Juup Heynckes playing Javi Martinez as a defensive midfielder, but they have been competing without one since he left. Juventus have essentially been playing with three central midfielders, or Marchisio who was converted from an attacking midfielder to what is essentially a deep lying playmaker when he has been fit.
For this season, Pep Guardiola noticed that he had to replace his aging fullbacks.....and he bought three fullbacks and a goalkeeper. He then changed his formation to better shield John Stones and that is something that is now being seen even though it is early days in the league. Personnel may have changed, the formation may have changed, but the philosophy has remained the same so that there is a bridging between how the team goes about business on the pitch and the results that they aspire to achieve.
Some say that a goalkeeper that comes off his line early would be so much better than Mignolet......I have even read of how that ought to be Karius in the interim. A better striker, a better keeper with the same setup does not solve the problem that is in midfield, defensive lapses in the backline. You would essentially facing the same problems thinking that you can outscore teams.
I said this in another post. Liverpool has 2 clean sheets in 10 games this season, 2 clean sheets in 12 if you were to include the qualifiers. In short, you are in a situation where have to plan on how you are going to score a minimum of two goals in every game to try and get a win, and at times, that may be good enough for just a draw.
As for the pressing, there was an article in The Times.
https://www.thetimes.co.uk/article/klopps-pressing-problem-x53dq6zhhThere is a huge difference when it comes to having a single game per week, and playing youth in cup games, to having to play your first team in the Champions League, having to travel outside the country as opposed to going Swansea as the furthest destination once a year.....several times if you draw them in the cup. Rodgers hit this wall when the team had extra games to play, Antonio Conte generally struggled with it even when he was at Juventus, and in the time that Klopp has been here, he has struggled with multiple games.
Some of these problems can be solved only by hitting the market and doing business that makes sense. The team needed a CB or two, a starting LB. None of those materialized, Matip is less reliable, Lovren and Klavan still make the same mistakes, and with Arnold and Gomez starting well, they soon hit a dip yet some would argue that this is a department that does not need investing? Not for me.
There are days when your attack is not up for it, these happen; in those days, one needs the defense to hold firm and hope that forwards/anyone can take care of one or two good chances that each team gets a game. If not, you will be looking at an uphill struggle each and every season.