PSG drew level 1-1 on aggregate at Anfield through Ousmane Dembele, which eventually took the round of 16 tie to penalties at Anfield.
In the shootout, Gigio Donnarumma reclaimed his reputation as he made saves to deny Darwin Nunez and Curtis Jones, before Desire Doue fired home to seal a 4-1 win.
Afterwards, Enrique declared: “It does not matter if we deserve the win. Both teams deserved to go through. We were better in Paris and they were better here. My team showed great personality and character at Anfield. The atmosphere was great and it was tough.
“When the draw came out as Liverpool against Paris, both managers thought the same: one of the best games you can watch in Europe. The Champions League has nothing to do with consistency. You have to be great in moments. We suffered a lot. They suffered a lot.”
Meanwhile, skipper Marquinhos also said: “It was a very tough match. We had to dig deep and it was very difficult, but we did all we could to win the tie. Liverpool demand a lot from you. They’re a very strong team. Now we’re in the quarter-finals and need to be ready for another difficult tie.
"It's a special day for us, to come here and win with this young team. The coach, the staff, everyone is doing a great job. The sky's the limit. We can't stop here – we still have work to do. We need to recover and think about our next match (against Marseille on Sunday)."