Roma overturned a 4-1 first leg lead in shocking fashion, beating the Catalan side 3-0 at the Stadio Olimpico and progressing on away goals on Tuesday.
The Serie A side lost their prized asset Salah to Liverpool in the summer, with the Egypt international moving to Anfield in a £34 million deal, and he has since gone on to score 39 goals in 44 appearances this season.
However, there is now a chance that the two sides could meet in the Champions League semi-finals, after Liverpool defeated Manchester City 5-1 on aggregate.
"I walked up the stairs and someone told me," Klopp said regarding Roma's progression.
"I thought it was a joke. Not that I don't respect Roma, they are fantastic team. I just wasn't expecting it, but knew it was possible.
"They lost Mo Salah and they are in the semis - it's a big thing!"
The draw for the semi-finals of the Champions League will be made on Friday 11 April at 12:00 BST.