But after watching them struggle to impose themselves on one of the prime candidates for relegation at The Valley on Saturday, it seems evident that Houllier still has plenty to do before Liverpool can compete with the big achievers on a regular basis.
It could be argued there were mitigating circumstances: Michael Owen, Jamie Redknapp and Paul Ince were probably suffering a hangover from England's morale-sapping defeat by France three days earlier; Jamie Carragher's controversial dismissal, Liverpool's second in two matches, led directly to Charlton's winning goal, Keith Jones taking full advantage of Liverpool's defensive disarray and Steve Staunton's uncharacteristic blunder; and Charlton themselves played with great spirit and determination.
But if Liverpool want to compare themselves with their greatest rivals, Manchester United, then none of this should be allowed to disguise their shortcomings. In order to cope with the vagaries of form, fitness and confidence they need a bigger squad, and while Carragher's supposed elbowing of Charlton striker Martin Pringle seemed, at the very worst, accidental and in all probability non-existent, a total of two genuine goal attempts prior to that should be Houllier's concern this morning rather than the possibility of an FA reprimand for labelling both Pringle and referee Mike Reed cheats.
"They've got too many prima donnas," one Charlton fan said of Liverpool on his way out of the ground, and he had a point. Ince and Redknapp in particular gave the impression it was all a bit beneath them and Houllier's hardest task will either be to coax some consistency out of his highest- paid players or replace them with others who are prepared to work hard.
Referee Reed, it has to be said, was a pain in the neck. He kept his coloured cards close to his chest in the first half, contenting himself with whistling for a succession of infringements that were apparent only to him but after half-time, it seemed, he could bear it no longer and flourished three unnecessary yellow cards in two minutes. When Pringle went down clutching his throat the red card was sadly predictable, but you have to wonder whether the referee actually saw the incident or just reacted to the Charlton player falling.
For Charlton, though, it was a happy end to a turbulent week following the floodlight fiasco that threatened to overshadow proceedings. It was their second home win in five days and, after looking dead and buried by Christmas, they suddenly have a genuine chance of survival. The atmosphere by the end at what was once the largest of all League grounds was like a carnival, and if any club deserves the luck that came their way on Saturday it would have to be Charlton.
"After the run we've had it would have put a lot of people down, but the fans and the players have been up for it all season," said their estimable young manager Alan Curbishley. Liverpool's players would do well to take note.
Goal: Jones (70) 1-0.
Charlton Athletic (3-5-2): Royce; Mills, Brown, Tiler; Robinson, Jones, Kinsella, Redfearn (Barnes, 68), Powell; Pringle (Bright, 85), Hunt. Substitutes not used: Newton, Barness, Ilic (gk).
Liverpool (3-5-2): James; Carragher, Matteo, Staunton; Heggem (Gerrard, 81), Redknapp, Ince, McManaman, Bjornebye (Song, 73); Fowler, Owen (Riedle, 81). Substitutes not used: Thompson, Friedel (gk).
Referee: M Reed (Birmingham).
Sending-off: Charlton: Carragher. Bookings: Charlton: Mills. Liverpool: Ince, Staunton, Bjornebye.
Man of the match: Pringle.