Sadio Mane's inspired spinning finish inside 26 minutes delivered just what the Reds were after and allowed them to seize control of a heavyweight encounter.
Sadio Mané scored twice in a superb individual display while the equally impressive Virgil van Dijk also scored in Liverpool's first European away win of the season, and arguably their finest under Klopp.
He said: "I see it like all the boys see it in dressing room and everybody who sees it with us, it is a big night". The second half I was really happy by how mature the performance was, how strong we looked, how good we defended.
In contrast, Bayern's defeat saw them exit the competition before the last eight for the first time since 2011, and Milner was pleased with the way Liverpool dealt with the Germans.
On the instructions from the manager, the centre-back said: "Obviously be courageous when we have the ball, make sure everyone wants the ball and when we defend, defend all together".
"We again set a mark for this wonderful club, that we really are back on the landscape of global top football".
GETTY IMAGESVirgil van Dijk outjleaps the Bayern defence to head in Liverpool's second goal from James Milner's cross
"We were playing at home but that wasn't our game and I think that's why Liverpool beat us".
"We're still on the way to win the Bundesliga and that's why you have to push forward". Andy Robertson also picked up a booking in stoppage time that means he will miss the first leg of the quarter-finals but they were the only blemishes on an otherwise impeccable night for Klopp's team. The Senegal global also headed in Liverpool's third of the night for his 10th goal in as many games in all competitions for the Merseyside club.
"Virg knows that he can play better than he did, especially in the second half, we played as good as is necessary and possible in a game like this".
"We defended pretty well, didn't give them too much, and the front three were outstanding again".
Kalank Teaser: A story of eternal love!
Recalling a story when he saved her from falling, Varun further said, "One day, I reached 20 minutes late for the shoot". The teaser of Kalank was unveiled at a grand launch in the suburban theatre of Mumbai today.
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