The Reds triumphed 2-1 on aggregate with Lautaro Martinez scoring the only goal at Anfield in the second leg, while Mohamed Salah hit the post twice.
One of the big talking points of the game was Alexis Sanchez’s red card, picking up two yellow cards for poor tackles.
Liverpool boss Jurgen Klopp said: “I don’t understand why we have to discuss that. If you played football, if you can win the ball only, if you bring yourself in a position that you endanger the opponent then you don’t win the ball. That’s it.
“If Fab (Fabinho) goes in with the same intention, with a long leg, then both players get injured. Fab is there because he judged the ball that if he is not flying in, then I will get it. But because Sanchez is flying in and yeah, he touched the ball - that’s possible - but in the end he cannot stop and hit Fab in a really bad way, to be honest.
“I think he was quite lucky that he didn’t get a different colour (card) in the first half for a foul on Thiago, leg that high against the knee, similar situation. Passion is good, absolutely good, but if it leads to these kind of things it just doesn’t help.”
Meanwhile, Bayern Munich also progressed to the quarter-finals with a stunning 7-1 home triumph over Austrian champions Salzburg who had drawn 1-1 in the first leg.
Robert Lewandowski had a hat-trick within 23 minutes, including two penalties, while Thomas Muller also scored a double, with Serge Gnabry and Leroy Sane also on the scoresheet.
Lewandowski said: “Everyone knew that we had to put our foot on the gas from the first minute and show our quality. Especially the first 45 minutes showed that we are extremely dangerous when we play a bit quicker and get the ball into the penalty area.
“We showed that today. It’s the Champions League and that’s always special. It’s important that our form continues to improve at this important stage of the season.”