The Blues were unable to lay a glove on the Premier League champions, and their task was made even harder when Andreas Christensen was sent-off just before half-time after denying Mane a goalscoring opportunity.
The Senegalese superstar then scored two goals in four minutes shortly after the restart.
Liverpool were gifted their second by Kepa when the Spain international's pass was intercepted by Mane and subsequently returned into the back of the net.
Jorginho stepped up to take the spot-kick but was denied by Alisson with a fine save.
He told BBC Sport: "I thought we could get higher up the pitch and would have done with 11.
"I was concerned with how we would defend our box, first half we were brilliant at doing it but the red card changed the whole course of the game."
He added: "For chances the first half was very even. The red card changes the face of the game, the talk I do at half-time, it forces me into a reshuffle and it was always going to be difficult after that.
"I think it could be given or not. I was perhaps surprised it was given as a yellow first. If it was given as a red straight away and you continue with that.
"We showed moments on the counterattack when we were dangerous in the first half. My team talk was be more confident on the ball then the red card changes the whole team talk."