Ousmane Dembele struck early to draw the aggregate score level at 1-1 and with no other breakthrough through to extra-time, the round 16 tie went to penalties.
PSG goalkeeper Gigio Donnarumma denied Curtis Jones and Darwin Nunez to win the shootout for the visitors.
Carragher later told CBS: "I am a bit deflated about the result but listen, the best team won—PSG.'
"We saw how they performed in the first leg to make it 1-0. I called it a robbery. In this game, I thought the first 20 minutes to half an hour, I felt like Liverpool were going to go on and win the game comfortably. They just couldn't get that goal early on. They had two or three chances they didn't put away, then PSG got that goal.
"For the rest of the game, it felt nip and tuck. In extra time, it just felt like PSG took over really. Where I was in the Kop, we were all just desperate and hanging on for penalties really. But even that wasn't a given—it's a lottery and anything can happen."
Carragher was full of praise for the home crowd, who he believed gave everything on the night.
He continued: "Listen, the atmosphere was brilliant tonight. I was in the Kop with my mates but we just didn't get the goal to go mad. I think we had a couple—there was one disallowed, I think, and one hitting the inside of the post, so we were going mad then.
"I thought in the second half, we were attacking the Kop and I thought that would be a little omen that we would get the winning goal, but we just ran out of steam. We were just hanging on really.
"I thought the left-back (Nuno Mendes) against Salah was outstanding again. He's been brilliant in the two games. I think the two midfield players, Vitinha and Neves, were brilliant.
"I thought for the first sort of hour, maybe a little bit more—maybe 70 minutes—it was a brilliant game from both sides."