The Reds overturned a 3-0 deficit to win the tie 4-3 after victory at Anfield.
"After the game, we lined up arm-in-arm in front of the Kop together and sang 'You'll Never Walk Alone' with the fans," Matip told 11Freunde.
"That was one of the most beautiful moments of my career, maybe on the same level as my debut for Schalke in Munich.
"I didn't care about anything; I was floating on air after singing with the fans."
Matip went on to add: "And when I came into the doping test room, there was a guy sitting there pretty depressed – Lionel Messi.
"You know each other from the pitch, but it's not like you sit around with them every day in a small room like you're getting coffee.
"Everyone is celebrating, and I'm sitting in a cubicle with Messi."