Yesterday at Anfield they might as well have unpicked the sponsor's name from their shirts and replaced it with "relegation" because they reek of failure, but after 12 defeats in 16 matches they have every right to.
Wilson was his usual epitome of optimism afterwards but it is getting harder to locate its source. "We were a bit harshly treated," he said. "We didn't deserve the four goals, to be honest, and I'm still confident we can get out of it. Sixty-six points is a lot to play for and the teams we have to play are in the block above us. As long as we retain out confidence we're capable of escaping."
Brave words, but they have been heard before. The galling thing for Wilson yesterday was that Wednesday took the lead through Niclas Alexandersson and were then swept aside by the quality of the goals if not the supremacy of Liverpool's play.
It is a recurring theme. Wednesday do not look the worst team in the Premiership but their results do, and on this occasion it was Sami Hyypia, Danny Murphy, Steven Gerrard and David Thompson who rammed home the unfairness of that fact of life.
Wednesday began with an explosive 19th-minute goal. Wim Jonk, whose elegant skills deserve better, shaped to cross a free-kick but rolled it slowly across the area. Liverpool realised the danger too late, and as their defenders charged out Alexandersson crashed the ball in the opposite direction, comprehensively defeating Sander Westerveld.
If the Owls could have held that lead to allow it time to absorb into their self-belief the result might have been different, but they have made a habit of surrendering advantages and within two minutes they did so again, Hyypia rising above Andy Booth to head into the opposite corner.
Having got the equaliser, Liverpool maintained their momentum and spent the rest of the first half pounding away at the Wednesday ramparts. After 33 minutes Thompson's header looped just over, and five minutes later only a goal-line clearance by Jonk denied Michael Owen.
The visitors were being stretched by their opponents' movement and with the safety of half-time looming they cracked. The space for Rigobert Song's throw-in was created by Titi Camara's dummy, and as Wednesday were caught on the wrong foot Thompson thumped a volley that was stopped spectacularly by Kevin Pressman. The save deserved a better fate, but Murphy's agile effort flashed past him.
Liverpool can be the most infuriating of teams and their performance declined immediately after the interval. But for Westerveld's finger-tip save from Alexandersson Wednesday would have equalised within 90 seconds of the restart. The Swedish winger also scraped a post with a shot after 65 minutes.
Even the somnolent Liverpool woke up after that, their younger players taking up the challenge. The 19-year-old Gerrard produced a mazy run that was reminiscent of Steve Heighway in his prime. Receiving the ball 40 yards out, he glided past one challenge and accelerated to round Des Walker and slide the ball past Pressman. In most matches that would have eclipsed the other goals but Thompson came close to matching it, teasing Lee Briscoe and then curling a left-footer into the corner.
The Wednesday fans' last retort was a repeated chant of "Barmy Army". But after retaining their optimism while watching their team gain six points from 16 games, they would have to be.
Goals: Alexandersson (18) 0-1; Hyypia (20) 1-1; Murphy (41) 2-1; Gerrard (68) 3-1; Thompson (79) 4-1.
Liverpool (4-4-2): Westerveld; Song (Carragher, 73), Henchoz, Hyypia, Matteo; Thompson, Hamann, Gerrard, Murphy (Staunton, 76); Owen (Fowler, 80), Camara. Substitutes not used: Meijer, Friedel (gk).
Sheffield Wednesday (4-4-2): Pressman; Nolan, Thome, Walker, Briscoe (Sibon, 80); Alexandersson, Atherton, Jonk, Rudi (Quinn, 89); Booth, De Bilde (Cresswell, 78). Substitutes not used: Haslam, Srnicek (gk).
Referee: P Durkin (Portland, Dorset).
Bookings: Liverpool: Thompson, Henchoz. Sheffield Wednesday: Thome, Rudi.
Man of the match: Thompson.