This is the first time since 2011 that Bayern have failed to make the quarter-finals in Europe's top club competition.
"We still have space for improvement but beating Bayern here is a big one". But while the Senegalese forward maintained his hot streak by taking his recent goal haul to 10 in 10 games with his double against Bayern - and remarkably half of all 16 goals the Merseysiders have scored in their eight games since the start of February - the real star of the show for Liverpool was Van Dijk.
"We all feel that's where this club belongs and we proved it at least a little bit".
"It's a hard place to come, not too many teams have wins on their card at Munich". It was also a display of muscle-flexing by City, Liverpool and Spurs that will have been noted by the likes of Barcelona and Juventus, the two continental heavyweights most likely to stand in the way of an English triumph in the final in Madrid on June 1.
The Reds may not have always been at their very best on the ball at the Allianz Arena, but they pulled off a performance that outlined their growing maturity.
"But we kept them as often as possible away from our goal".
GETTY IMAGESVirgil van Dijk outjleaps the Bayern defence to head in Liverpool's second goal from James Milner's cross
"It's the first step to win a game like this".
"You have to find different ways".
"I thought they were as bad as I've ever seen". I'm really happy about the result. "We have a lot to improve, a lot to learn, but we are back and I like that very much".
When he was told after the 3-0 win, which secured a 3-2 aggregate victory for the Italians, that Juve had never managed such a comeback in the Champions League, Ronaldo said, "Maybe that's why they signed me".
In the last three seasons Liverpool have faced German clubs, they have won the tie and gone on to reach the final: the Champions League in 2005, the Europa League in 2016 and also last season.