The Reds scored a 2-0 away win over RB Leipzig in the first leg of their Champions League last-16 tie.
Mane admits Liverpool are now out of the Premier League title race, instead focusing on success in Europe.
"Beyond the top four is now, right now, our main target. But the Champions League, that is our main, main, main target. To win it, not be second, but it won't be easy," the 28-year-old went on.
"You're going to face the best teams in Europe, but we're here to beat the best in the world. We'll do everything possible to go forward and win the Champions League."