Blackburn never got started, were three down within half an hour and were lucky the final scoreline did not look much worse. Most worryingly for Souness, Rovers played like a team in mid-table security. The reality is anything but.
With seven games remaining, only four clubs are below them. One of those, Portsmouth, are a point behind with a game in hand and if Leicester City defeat Leeds United tonight, only a marginally superior goal difference would prevent Rovers from dropping another place.
"We were well and truly bashed up day," was Souness's frank assessment. "Our game plan didn't last 10 minutes and 4-0 didn't flatter them. Once we went three down it became a case of trying to preserve our goal difference.
"We find ourselves in a very precarious position and we fully realise the danger we're in. It's 'stand up to be counted' time and I believe in my players to get us out of trouble."
Liverpool, meanwhile, gratefully accepted an effortless victory that lifted them back into fourth position. "It was a strong, powerful and determined performance," said Gérard Houllier, the Liverpool manager.
Last season, they travelled to Chelsea on the last day with the winner qualifying for the Champions' League. A repeat of that situation seems inevitable when Newcastle United travel to Anfield in the corresponding fixture this time around.
By then, Michael Owen's contract talks - always scheduled for April - may well have been resolved. If the Liverpool board needed any reminding of his worth, his 15th and 16th goals of a truncated season provided it. Houllier remains optimistic, if not convinced, that he will sign an extension.
Liverpool may not be in line to win any trophies this season but Houllier continues to describe their remaining fixtures as "cup finals". His team had evidently understood the message, because they were ahead within seven minutes, Blackburn having hardly enjoyed so much as a kick.
Emile Heskey killed Harry Kewell's hopeful poke forward and took the ball to the edge of the Blackburn penalty area. Owen had pulled away into space and accepted the pass, with Brad Friedel unable to prevent his first-time shot rolling beneath him.
They were handed a two-goal advantage 15 minutes later. El-Hadji Diouf provided a cross - more in hope than expectation - and Andy Todd's miscue sent the ball spinning beyond Friedel.
The third followed soon after as Blackburn threatened to cave in. Owen collected Diouf's pass before emphatically crashing a drive into the far corner from the edge of the area.
Despite a pair of half-time substitutions, Blackburn gave no indication of getting back into the game. Craig Short and Garry Flitcroft were the men withdrawn, but it could have been virtually anyone. Jon Stead was the honourable exception. The former Huddersfield Town striker never stopped chasing lost causes all afternoon.
Even playing at little more than half-pace for most of the second half, Liverpool continued to trouble Rovers' labouring defence. As ever, Steven Gerrard drove them forward with relentless enthusiasm. His performance was typified by a thrusting run from midfield late on, only curtailed when Nils-Eric Johansson fouled him on the edge of the penalty area.
Milan Baros, who replaced Owen as a late substitute, then presented Heskey with his 10th goal of the season following good work from Kewell.
Danny Murphy twice, John Arne Riise, Baros and Kewell all went close late on but Liverpool eventually had to settle for converting just four of more than 30 chances. "Not bad for a boring team," Houllier said. It was Liverpool's most emphatic victory of the campaign - and undoubtedly the most facile.
