They fell down on the task, just as they did at Old Trafford last week. When Rivaldo's free-kick deflected off Milan Baros and looped high into the Liverpool area, Stoltidis rose above Sami Hyypia to head beyond Jerzy Dudek's despairing dive.
The manager refused to apportion blame, however, saying: 'People will make a lot of the goal coming from a set-piece, but to be fair to Sami, the deflection didn't do us any favours and made it difficult as he jumped with their player.
'Even so, I'm very disappointed with the performance and result. The problem was in the first half, when we simply did not retain possession.
'We played better in the second and created more opportunities. There were more situations for us near their box, but when you're losing 1-0 to an aggressive team who fight for every ball, it is difficult to find space.
'Now, the group looks very open and perhaps our home games will prove most important in helping us to qualify.'
With a raucous support and a stream of deafening firecrackers, the last thing Liverpool needed to do was give Olympiakos' players any extra encouragement.
Yet, livewire Ioannis Okkas was allowed space in the third minute to control a long though-ball in the area and wriggle past Hyypia before drilling a shot against the near post. If that was an early warning, it went unheeded as Liverpool needlessly conceded a free-kick 30 yards out and then saw Rivaldo add a touch of creativity to a remarkable tally of 24 goals in 57 Champions League appearances.
Finishing off chances has always been the former Barcelona great's forte, but he showed he can lay them on for others as well with the setpiece delivery that resulted in Stoltidis's winner. Liverpool have seldom been overrun as they were in the first half. The sight of the normallyanimated Benitez with hands deep in pockets indicated that suggestions for stemming the tide were in short supply.
Flashes of vintage Rivaldo only added to the discomfort as he crashed a volley narrowly wide, with minimum backlift but maximum power, and gave Hyypia the slip with an impudence that only the most gifted can muster.
The Liverpool skipper arrived a fraction late for what he believed would be a 50-50 challenge and paid a humiliating price as Rivaldo nutmegged him before continuing on his way.
For all Liverpool's improvement after sending on Harry Kewell for Stephen Warnock at the start of the second half, they could still have gone further behind when Stoltidis beat Dudek to Rivaldo's 75thminute corner and headed against the bar.
Defender Anastasios Pantos's 82nd-minute dismissal for a second caution gave labouring Liverpool a misplaced glimmer of hope. Quite right, too.
Benitez does not often show his emotions, but we might just have seen him blush had he taken a point from a performance like this.
