Van Dijk and co kept out Bayern’s attackers from scoring beyond a single goal in both legs, with the solitary one also coming via an own goal from Joel Matip who could not do much apart from turning in the cross from Serge Gnabry.
However, Klopp was full of praise for the Dutchman, revealing that the player has had a great influence on the entire squad since he moved to the club in last season’s January transfer window.
According to Goal, Klopp said: "It was brilliant. He was involved in the goal of Bayern as well, so what a night! What can I say? I could write a book about his skills, his strength, how much I like him, what a fantastic person he is.
"He is so young, already so mature, really strong, all good. Virg knows he can play better than he did tonight; we can play better than we did tonight. Tonight we played - especially the second half - as good as necessary and as possible.
"It is a difficult place to come and not a lot of teams have on their cards an away win at Munich. We have that now and that's cool. Difficult but cool."
It remains to be seen if Liverpool can repeat the performance of last season and reach the finals again, even as they compete with Manchester City for the Premier League title.