Sadio Mane acrobatically fired an effort over the bar and hit the post in a generally tame first half that also saw Dejan Lovren head narrowly wide.
Reds boss Jurgen Klopp was satisfied with the result: "We did the job and that was it tonight.
"It wasn't the most exciting game but we controlled it, had a few chances, got a clean sheet and gave some boys some minutes. I am pretty sure it is rare to have a game like this in the knockout stages.
"We needed to be serious and we were so all good. Of course, we want to win two games at this stage. When you watch the game you always think 'oh come on, a little bit more here or there' but they did well and it is all good. The attitude was outstanding."
He continued: "Adam [Lallana] needed a few minutes to get into the game but then it was really good and very important for him to play that long. He played 90 minutes by the way.
"Danny Ings got 30 minutes in the Champions League too which is nice for him. He knows he could have scored but I am happy for him.
On potentially drawing an English team in the quarter-final, he added: "I don't mind to be honest. I don't care. We take it how it comes. We don't wish for anybody. We played whoever we get. That is how it is. There are five English teams in and at one point we will play them so we will see when it comes."