Two notes before we get to the graphic.
One, yes, I'm counting penalties. It's probably not fair, but I reckon the easiest distinction is goals from open play versus goals that weren't. It also doesn't fundamentally alter the totals. Two, the stats are from my game notes (if I have game notes), or match reports from the official site, BBC, or the Grauniad (depending on who actually described the goal). I might be missing some, but I've double-checked in almost all cases. My memory's admittedly not the best.
Conclusions? Well, those numbers suggest it's the players, not the system. Liverpool was fairly consistent – and fairly good – over Benitez's first three seasons. Then the number surged in '07-08 (although Liverpool conceded far more penalties that season – six – the percentage is still the highest without spot kicks), and stayed "above average" in '08-09.
What's the difference between then and now? First and foremost, Hyypia stopped being a regular starter. He's considered one of the best defenders in Liverpool history for a reason. Second, Liverpool hasn't been helped by Carragher's aging; he still provides some amazing last-ditch tackles, but he's lost a step, especially in the air, and Hyypia was easily his best partner. Liverpool conceded less from set plays in '07-08 after Skrtel arrived, but not few enough.
Those are the only conclusions I can come to. If "zonal marking" was the problem, you'd expect Liverpool to have conceded the most in '04-05, when it was a new system. But it actually "worked" for the first three seasons, only to see the number of set piece goals rise around 2007.
The complete stats:
04-05
0-1 Graz (Tokic, corner); 0-1 United (Silvestre, from FK); 1-2 United (Silvestre, corner); 0-1 Olympiakos (Stoltidis, from FK); 0-1 Chelsea (J Cole, from FK); 0-1 Brum (Anderton, corner); 0-1 Boro (Riggott, from FK); 1-1 Villa (Solano FK); 0-1 Olympiakos (Rivaldo FK); 0-1 Charlton (Bartlett, corner); 0-1 Brum (Pandiani pen); 1-1 Chelsea LC (Gerrard OG, from FK); 0-1 Newcastle (Robert FK); 1-1 Pompey (Kamara, corner); 0-1 Arse (Pires FK); 0-1 Milan (Maldini, from FK)
05-06
0-1 CSKA Sofia (Iliev, from FK); 0-1 Chelsea (Lampard pen); 0-1 Bolton (Jaidi, from FK); 1-3 Luton (Nichols pen); 0-1 United (Ferdinand, from FK); 0-1 Chelsea (Gallas, corner); 0-1 Benfica (Luisao, from FK); 2-1 Everton (Cahill, corner)
06-07
0-1 Sheffield (Hulse, from FK); 0-1 Bolton (Speed FK); 3-1 Reading LC (Bikey, from FK); 4-3 Reading LC (Long, from FK); 0-3 Arsenal (Gallas, corner); 1-2 Galatasaray (Buruk, corner); 1-2 Arsenal LC (Baptista FK); 1-2 Newcastle (Solano pen); 0-1 United (O'Shea, from FK); 3-1 Arsenal (Gallas, corner); 0-1 Milan (Inzaghi, from FK)
07-08
1-1 Villa (Barry pen); 1-1 Chelsea (Lampard pen); 0-1 Porto (Lucho pen); 1-1 Reading LC (Convey, corner); 2-2 Reading CC (Halls, corner); 0-1 Everton (Hyppia OG, corner); 1-1 Cardiff (Purse, from FK); 0-1 Reading (Hunt pen); 0-2 Reading (Doyle, from FK); 0-1 United (Tevez, corner); 1-1 Derby (McEveley, from FK); 1-1 Wigan (Bramble, from FK); 1-1 Villa (Harewood, from FK); 1-2 Villa (Aurelio OG, from FK); 0-1 Havant (Pacquette, corner); 0-1 West Ham (Noble pen); 0-1 Boro (Tuncay, from FK); 3-1 Bolton (Cohen, corner); 0-1 Reading (Matejovsky, from FK); 0-2 United (Ronaldo, corner); 0-1 Arsenal CL (Adebayor, corner); 1-1 Arsenal (Bendtner, from FK); 0-2 Brum (Larsson FK); 2-1 Chelsea CL (Lampard pen)
08-09
1-1 Crewe LC (O'Connor, corner); 0-2 City (Garrido FK); 1-1 Spurs (Carra OG, corner); 3-1 Blackburn (Santa Cruz, corner); 0-1 PSV (Lazovic, corner); 0-1 Hull (McShane, corner); 2-1 Newcastle (Edgar, corner); 1-1 Everton (Cahill, from FK); 0-1 Everton FA (Lescott, corner); 1-1 Wigan (Mido pen); 1-2 Pompey (Hreidarsson, from FK); 0-1 Boro (Alonso OG, corner); 0-1 United (Ronaldo pen); 1-1 Chelsea CL (Ivanovic, corner); 2-1 Chelsea CL (Ivanovic, corner); 2-2 Chelsea CL2 (Alex FK)