"The first goal was ridiculous really, how he finished it off, the calmness and the finish", Milner told reporters.
"We still have space for improvement but beating Bayern here is a big one". "It does not bring back for me the other results from when we played them and we lost", he added.
Bayern's last Champions League triumph came in 2013 as they defeated Borussia Dortmund at Wembley, but since then they have never been able to get across the line in Europe.
Lyon's Lucas Tousart gave the visitors hope with a goal in the 58th minute, but Messi scored again in the 78th before passing for Gerard Pique and Ousmane Dembele to round off the win.
"It's a big, big step for us". We set a mark for LFC tonight that we are back on the worldwide landscape as a football club.
GETTY IMAGESVirgil van Dijk outjleaps the Bayern defence to head in Liverpool's second goal from James Milner's cross
"We knew they would attack a little bit more and we would have more spaces to play and we used it as well".
"I am really proud of the boys because it is a massive achievement".
"Today also I think we didn't try to play offensive and try to score the goal because we didn't have a lot of chances also and that was our problem today". 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. 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.
"I'm not happy, I'm angry because we know we should do better but we didn't".
"It's a hard place to come, not too many teams have wins on their card at Munich". "Bayern has so much quality, unbelievable, and we impressed them and that's a massive thing". It's not sweeter for me because it's Bayern.More news: Ethiopian Airlines Flight Crashes With More Than 150 On Board
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