The English top team had a 1-0 lead at home to Anfield after substitute Harvey Elliott's late deciding goal in the 87th minute at Parc de Princes last week.
In Tuesday evening's match, it took only just over eleven minutes before Ousmane Dembélé had made it 1-0 for Paris Saint-Germain. The lead held out regular time, which led to an extension that eventually became goalless.
The round of 16 had to be decided on penalties.
Liverpool's penalties from Darwin Nunez and Curtis Jones were both saved by PSG's outstanding goalkeeper Gianluigi Donnarumma.
PSG's 19-year-old substitute Désiré Doue scored the decisive penalty that took the French team further after 4-1 in the penalty shootout.
This was the best football match I've ever been involved in. It was an incredible performance, said Liverpool coach Arne Slot after the match and simultaneously stated:
Our luck ran out after last week.
In the quarterfinals, either Aston Villa or Club Brygge await PSG.
