With the first leg of a last-16 showdown between two heavyweight outfits having delivered a 0-0 draw at Anfield, everything was put on the line during a return date at the Allianz Arena.
Bayern would have been looking to dominate on home soil, but rather fluffed their European lines as Van Dijk and a double from Sadio Mane sent them crashing to a 3-1 defeat as the Reds marched on.
Klopp had been looking for a big performance from his side on German soil, and got what he was after as the Premier League title hopefuls put down another marker in continental competition.
Van Dijk told Liverpool’s official website of the message passed on by an ambitious boss: “Obviously be brave when we have the ball, make sure everyone wants the ball and when we defend, defend all together.
“Be brave when we are defending as well and sometimes go one-v-one, and I think especially the second half we did very well.
“We knew it was going to be very tough. At home they showed us a lot of respect with the way they played because that’s not the way they play.
“We knew they would attack a little bit more and we would have more spaces to play and we used it as well.”
Pressed on whether the Reds delivered a faultless Champions League showing, Van Dijk added: “Very close. I think to perform like we did, especially after our away results in the group stages, was very important.
“We knew how they would definitely set up and how they would probably come for us as well, and I think we did fantastic.
“[To celebrate with the fans] was unbelievable. They come everywhere we go and it’s always a great feeling to play for this club and I’m proud to wear this shirt.”
While saluting the away support, Van Dijk also reserved praise for fellow goalscorer Sadio Mane, with the Senegalese having been in prolific form over recent weeks.
The Dutch defender said of a forward who opened the scoring against Bayern with a stunning spinning effort: “Sadio has been at a different level these last weeks, months, and he is having a fantastic season.
“To score that [first] goal is obviously a big blow for them because they have to score two and for us we were then unlucky to concede the equaliser, but the second half was outstanding.”