Joel Matip's own goal levelled matters before half-time but Liverpool kept their illustrious hosts at arm's length throughout the second period, when Virgil van Dijk restored their lead before Mane headed his second of the game.
But, after a goalless first leg, they showed their superiority over their opponents in Munich.
"So even playing away from home, we worked well during the week, we were confident for the game here".
"But the truth is that I don't think Bayern knew what they wanted to do".
"It was brilliant", he said when asked about Van Dijk's performance, per Goal. There are some places in world football that whatever team comes here - Manchester City, Real Madrid, Barcelona - they wouldn't expect to win it.
"We still have space for improvement but beating Bayern here is a big one".
"We again set a mark for this wonderful club, that we really are back on the landscape of global top football". The only shadow is Hendo twisting his ankle, but it is Hendo so hopefully not too serious. He was so strong, so important to us, but he can play better than he did [on Wednesday].
The Fiver: sign up and get our daily football email.
Mane's opener was scored with a wonderful finish midway through the first half, but question marks will be asked of Manuel Neuer, who had rushed out and who left an open goal for the Liverpool striker to aim at, admittedly from a tight angle. I don't know about the statistics, but my impression is that there were not too many hard situations in and around our box.
"But, to be fair, we did have top centre-halves at the time as well". I could write a book about his skills, about his strength, how much I like him, what a fantastic person he is, ' said the Reds boss of his £75million man. "It's just a good moment for Liverpool and let's enjoy that".