Liverpool won 1-0 in the first leg thanks to Harvey Elliott's late goal in Paris. But in the return match, PSG leveled the gap when Dembele scored to help PSG win 1-0 after 120 minutes of play.
The French team won 4-1 in the penalty shootout when Darwin Nunez and Curtis Jones of Liverpool missed a shot. On PSG's side, all 4 of their players successfully implemented it.
"It was the best football match I've ever played in. The team's performance was incredible, especially compared to last week. In the first 20 to 25 minutes, we overwhelmed them, creating one chance after another and we suddenly fell 0-1. Maybe we are out of luck.
After 90 minutes, we felt we deserved a better result, instead of being behind 0-1. Except for the last 5 minutes of the second half, PSG overwhelmed us, creating 1-2 chances, while Liverpool had a perfect match, except for scoring. PSG did the same last week when they played a perfect game and didn't score, and that happened to us today, Arne Slot said bitterly after the match.
Liverpool have finished the Champions League group stage at the top of the table, winning seven of their eight games and losing just once in the Premier League this season. They were once rated as having a chance to win the treble for 4 seasons this season, but were eventually eliminated in the Champions League and FA Cup.
"It's unfair to say goodbye to the tournament in the 1/36 round. Your team tops the table again and faces PSG, one of the strongest teams in Europe, but that is also a great thing about football.
People around the world love to watch this match and the gap is very small, and if you want to win, you have to be a little lucky. We were lucky last week, I didn't think we were lucky today.
Now we know what we have to do for the rest of the season, which is towards the League Cup final and the other nine Premier League games, Slot added.
Meanwhile, Liverpool captain Virgil Van Dijk has called on his teammates to ignore being left out of the Champions League, in the hope of a League Cup final against Newcastle at the weekend.
Van Dijk said: "It was a very tense match, it's clear Liverpool played completely differently from what we showed in Paris but unfortunately we had to lose on the penalty spot.
I told my teammates that you can be disappointed because Liverpool have been eliminated from the UEFA Champions League, please lift your heads and prepare for the next match. It was a great challenge at the weekend, so we will continue to move forward.