Rafael Benitez admitted that his side had enjoyed a lucky escape after watching them win a thrilling FA Cup tie 5-3 at plucky Luton.
The Premiership high-flier at one stage trailed its humble host 3-1 until the introduction of substitute Florent Sinama Pongolle sparked an extraordinary fight-back.
The Frenchman struck twice in the final 33 minutes and those goals, together with Xabi Alonso's spectacular brace, helped settle a dramatic game which will go down in FA Cup folklore.
But Benitez remained deeply unsatisfied with Liverpool's performance on a night which saw his ordinarily well-drilled defense torn to shreds by the Championship side.
"We thought it would be easy after we scored the first goal and we gifted them lots of opportunities," said the Reds manager.
"We have qualified but we have to learn that when we are better than our opponents, we must finish the game," he said.
"If you cannot play because of the state of the pitch and because the opponents are being very aggressive in midfield, you have to spread the game wide and play more long balls," the Spaniard observed.
After 53 minutes, Liverpool seemed certain to fall to another humiliating domestic cup exit, to add to last year's defeat at Burnley and this season's loss to Crystal Palace in the League Cup.
Luton had shrugged off the effects of Steven Gerrard's brilliant 15th-minute opener to level through Steve Howard's cool finish and then forge ahead with Steve Robinson's superb spin and shot just before halftime.
Benitez's world then threatened to crumble completely at the start of the second half when first his French striker Djibril Cisse missed a penalty, awarded for Paul Underwood's foul on Gerrard, and then Luton scored one of its own courtesy of Kevin Nicholls, who converted after Rowan Vine had been felled by goalkeeper Scott Carson.
But then Pongolle changed the game.
The French youngster cut the deficit with a precise finish from Gerrard's pass, and Xabi Alonso equalized with a magnificent dipping shot moments later.
Luton's self-belief had finally been broken, and it was no surprise when Pongolle completed the comeback by heading home in the 73rd minute.
Alonso even put a flattering gloss on the scoreline with a bizarre fifth goal in injury time, the Spaniard rolling in from 65 yards after the Luton goalkeeper Marlon Beresford had ventured forward for a corner.
Luton manager Mike Newell was proud of his team's performance against the reigning European champions, but still rued their generosity in allowing Liverpool a route back into the game.
"We've got to learn that at 3-1 up, we should be killing the game off," he said the Hatters boss, himself a Liverpudlian.
"We were the better team in the first half and I told my players that at halftime. But I never thought that the game was dead because Liverpool have got too many quality players."