The game sprang to life after the 20-minute mark and it was Liverpool that drew first blood when Mane expertly settled a Virgil van Dijk long ball, spun back to his right and chipped into an open net after Manuel Neuer was drawn off his goal line.
"Scoring three goals here is massive and a big step for us, a big, big step", the former Borussia Dortmund manager said.
"We all thing that's where this club belongs and tonight we proved it at least a little bit. It does not bring back for me the other results from when we played them and we lost", he added. "I don't know why because sometimes we tried to push Liverpool but it was two versus four players and that's why we didn't create much - and that's not our game".
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GETTY IMAGESVirgil van Dijk outjleaps the Bayern defence to head in Liverpool's second goal from James Milner's cross
"It is a hard place to come and not a lot of teams have on their cards an away win at Munich". Playing your best football, free-flowing, is not possible against this team because you can not use your speed really.
"I think we played too deep and didn't want to make too many risks".
"He is so young, already so mature, really strong, all good". We wanted to play more football than we did in first half, and we changed and did that in the second half much better.
"In the first half we scored an outstanding goal - wow - and by half-time time everybody knew it would not be easy for Munich, and that is important information for the opponent after they were happy with a 0-0 at Anfield". It's not sweeter for me because it's Bayern. I wanted to win for Liverpool, not to beat Bayern. "It's just a good moment for Liverpool, so let's enjoy that".