The visitors scored early in the first half when a mix-up between Ibrahima Konate and Alisson allowed Ousmane Dembele to bundle the ball home.
With the tie level after 90 minutes and extra time failing to separate them, both teams went down to a penalty shootout in front of the Anfield Road End.
Darwin Nunez and Curtis Jones both saw their spot kicks saved by Gianluigi Donnarumma to condemn Arne Slot’s side to an early knockout stage exit.
**Here were the key talking points from Anfield:**
Reds finally meet their match
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For a third season running, Liverpool have bowed out on the European stage.
On each occasion, they were outclassed; first by Real Madrid in the last 16, then Atalanta in the Europa League, but Paris Saint-Germain were different.
Unlike the surprise defeats to Nottingham Forest, PSV Eindhoven and Plymouth, the Reds faced a genuine equal for the first time in this campaign.
Arne Slot had warned his side that they would need to deliver their strongest performance to date in order to reach the Champions League quarter finals.
But they came up short in a contest played at a high intensity from the first whistle as Les Parisiens were the beneficiaries of a role reversal in the tie.
Just as their hosts did in last week’s first leg, Luis Enrique’s side snatched a solitary goal and were made to work for their extra time and penalty shootout.
The PSG manager forecast that whichever team progressed to the last eight would almost certainly be one of the finalists and it’s difficult to disagree.
Both teams gave no quarter until the very last as Liverpool discovered what numerous opponents have endured this term by finally meeting their match.
Slot now faces biggest test yet
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A maiden Wembley appearance should be the stuff of dreams for Slot.
Until now, his debut season in the Anfield hot seat has been largely trouble-free and looks set to end with a crowing moment in the Premier League title.
This result does, however, put a different complexion on the Dutchman’s powers of persuasion as Liverpool gear up for the Carabao Cup final.
An unrelenting 120-minute slugfest followed by the lottery of a penalty shootout is less than ideal preparation for Sunday’s clash with Newcastle.
Even before stepping up in front of the Anfield Road End, Slot’s players were visibly exhausted by the time referee Istvan Kovacs ended their stalemate.
Lifting them from that stupour ahead of a date with destiny in the capital is not simply a case of recharging the battiers after they were so heavily sapped.
Slot will also need to find a way to reinforcing the strong mindset that his players have shown this season fo face off against an injury-strewn Magpies.
This weekend promises to be the Liverpool head coach’s toughest test yet.
Injuries add to Anfield’s unease
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Crashing out of the Champions League right before a cup final was hard enough for Kopites to endure without adding injuries into the equation.
Yet Liverpool risk venturing to Wembley with increasing selection headaches after Trent Alexander-Arnold and Ibrahima Konate juoined the casualty list.
The homgrown vice-captain was visibly devastated by the ankle problem whichi limited him to a four-minute walk to the tunnel after being substituted.
Matters worsened when Ibrahima Konate became another premature exit which leaves Slot needing to reshuffle his back before taking on Newcastle.
With Conor Bradley and Joe Gomez still sidelined, while Alexander-Arnold facin an uncertain future, the onus will fall on Jarell Quansah at right full-back.
Konate’s direct replacement Wataru Endo can also slot into the centre-back void fairly comfortably, having operated adquately there already this season.
Yet what follows the pair in terms of viable alternatives will no doubt have Slot preoccupied as he prepares to lead his side out beneath the famous arch.
Once again out of necessity, Liverpool might have to turn to their burgeoning academy crop to help get them through another Carabao Cup showpiece.