Liverpool's win also dashed Pep Guardiola's hope of seeing Bayern, his former club, in the last eight.
Liverpool overcame Bundesliga leaders Bayern Munich in the Champions League last 16 inside the Allianz Arena on Wednesday evening, and after the match fans were quick to praise a star man in the victory.
"I was alone sometimes and I didn't have help, I couldn't do something and it was very hard", he said.
Bayern Munich are facing up to another season without Champions League glory after losing to Liverpool and Robert Lewandowski has made his unhappiness with his team's tactics clear.
"If you are alone against two or three good players it is very hard to play". Look at Manchester City, they are not [just] going for the title or the Champions League.
"Virgil gives organisation on set pieces, and he is risky", Klopp said with some understatement.
"I would've liked to have him at Liverpool [when I was there]". They know it is a very tough place to come.
Nothing, however, helped provide the goals. He rushed out of goal to let Sadio Mane score Liverpool's first.
But in Virgil van Dijk, Liverpool possess a player who has become so important and influential to Jurgen Klopp's side that he could prove to be the extra-special player who makes all the difference for the Anfield outfit this season, both in the Champions League and back home in the Premier League.
Three years ago, Bayern recovered from a two-goal deficit at halftime to beat Juventus 4-2 at the same stage of the competition. Liverpool got precisely what they paid for: the best. "This time we deserved to go out".
Bayern and Dortmund are now joint top of the Bundesliga table, with 57 points amassed from their allotted 25 games. Not since Bayern's Wembley win against Dortmund in 2013 has a Champions League been won without one of them in the victorious team and there has been no sign of either of them slowing up in this season's competition.