Gerard Houllier, the Liverpool manager, shuns championship talk, a la Arsene Wenger, and that objective may indeed prove a step too far on his road to recovery this season.
There is, however, a growing conviction, a new-found substance to Liverpool. They were always capable of giving someone a "hiding on their day." This hiding was administered after they had accumulated 10 points from their previous four Premiership matches and advanced to the fourth round of the FA Cup.
The consistency and optimism will be gauged when they meet Manchester United in that tie on Sunday, and Houllier's team should not travel to Old Trafford in trepidation.
Robbie Fowler's hat-trick will have bolstered a self-belief that was bound to be undermined by the Michael Owen phenomenon.
Equally significant for Fowler - and for Liverpool - was the understanding developed by the pair in the face of widespread scepticism. Owen was the provider for Fowler's 100th and 101st goals in League football.
Again, more meaningful examinations lie ahead, but confidence is a powerful agent, momentum a potentially irresistible force, winning an addictive drug.
Of course it might have been a different match, a different story, had Jones not dropped that corner kick midway through the first half. He could scarcely do a thing right beyond that point and in the second half, when he handed Liverpool two more goals, he had to endure the derision of his own supporters.
To his credit, the goalkeeper responded to ironic cheers with suitable humility and good humour. The fans' deeper concerns, you sense, are with the direction given by the manager, Dave Jones.
Injuries and suspension severely limited Jones's options but he left Matt Le Tissier on the bench for half the match.
When Le Tissier was unveiled he looked heavier and slower than ever. Even so, he produced most of the few uplifting moments for his side, including a beautifully delivered pass from which Egil Ostenstad scored.
Whatever their differences, Jones and Le Tissier have to forget them. Southampton's survival in the Premiership may depend on an accord of convenience and Le Tissier's full-time contribution to the cause.
Jones, who at the best of times has the public demeanour of a man who has lost a pound and found a shilling, is showing signs of inspirational bankruptcy. Southampton require not only a touch of Le Tissier's magic but also hypnotic leadership.
The opening pledge to leave behind in the dressing-room "all that was said there" dissolved as Jones expressed his discontent with his charges. He could neither comprehend nor forgive them for folding, and exonerated "only three or four players" from condemnation.
Jones approached the match with a system as intriguing as the personnel he employed. He operated with James Beattie as his sole striker, supported by Ostenstad and Wayne Bridge from wide positions. Hassan Kachloul was encouraged to break from central midfield.
In the event, Southampton had neither the quality nor the fervour to make the plan work. A gifted goal should not be the cue for annihilation, but that is precisely what it was.
Southampton's flimsy midfield was overrun and their defence was trampled underfoot just as easily and ruthlessly by the movement and the variety of Liverpool's attacks.
Liverpool will not be deluded that they have become supermen overnight. They will, however, feel they are back in the mainstream and perhaps two or three reinforcements away from comparison with the best in the land.
Goals: Fowler (22) 1-0; Matteo (35 ) 2-0; Fowler (36) 3-0; Fowler (47) 4-0; Carragher (55) 5-0; Ostenstad (58) 5-1; Owen (63) 6-1; Thompson (73) 7-1.
Liverpool (5-3-2): James; Heggem, Carragher (Kvarme, 78), Matteo, Babb, Bjornebye; Redknapp, Ince (Thompson, 72), Berger; Owen (Riedle, 72) Fowler. Substitutes not used: McAteer, Friedel (gk).
Southampton (4-5-1): Jones; Hiley, Monk, Lundekvam, Colleter; Ostenstad, Hughes, Howells (Oakley, 63), Kachloul, Bridge (Le Tissier 45); Beattie. Substitutes not used: Dryden, Ripley, Stensgaard (gk).
Referee: U Rennie (Sheffield).
Bookings: Liverpool: Carragher, Ince; Southampton: Monk, Colleter, Hughes.
Man of the match: Fowler.
Attendance: 44,011.Reuse content