Frankly, I am not entirely sure what Rodgers's desired style of play is, although if I had to guess I would say that it's some kind of superhuman fusion of the finest possession teams and the finest counter-attacking and pressing teams.
I think that's exactly what it is, without the perjorative use of 'superhuman' implying it's some sort of impossibility. There's been some discussion about the video SerbianScouser posted a few days ago, with the most obvious point being the drop in counter attacking between last season's Liverpool and this.
But that discussion so far has overlooked something else clear from the Prozone graphs: last season's Liverpool counter attacked (as a proportion of it's activities with the ball) far less than any Rafa side did. Yes, we counter attacked - we exploited over committed opponents, at pace and with precision. Yet we also kept possession of the ball at times; we had spells of dominance and possession with a slower attacking buildup. The Arsenal and Everton games are illustrating examples; yes, we counter attacked at will, and tore them apart. But in both games we'd opened the scoring through set pieces early, forcing the opposition to commit men forwards. It's very difficult to counter attack at nil-nil (or trailing) against an opponent that's happy to sit tight.
Last season, we opened the scoring in 28 of 38 games;
every one of those in the first half; 22 of them within the first half hour, 12 of them within the first 15 minutes. So far this, we've opened the scoring 21 times - 15 of those in the first half. That's going from the fastest starters in the league, to the 13th fastest (incidentally, City have gone from 2nd fastest to below average too, and similarly suffered in the table).
Again; how do you counter attack (literally, counter from an opposition attack), when the opposition doesn't need to attack?
You need to be able to create - and score - goals without the opposition leaving a nice 50 yards of open space for you to attack into. You need creativity, but you also need goalscorers. You need to be able to maintain possession, dominate the opposition and carve openings - as we did against West Brom for instance - and put them away; as we did not.
The best teams have always had the ability to score more than one type of goal; and not simply by sticking on a Plan B targetman. Plan A needs variety within itself. The best Liverpool sides always had this; the ability to dominate and probe; the ability to maintain and draw out the opposition; the ability to strike quickly and decisively at an opposition mistake or gap.