The Reds came into their Anfield meeting with Eddie Howe's side having secured a place in the semi-finals of the Champions League by twice defeating Manchester City.
But there was little chance of anyone taking their eye off the ball ahead of a return to Premier League action, according to the scorer of the hosts' first goal on what proved to be a comfortable afternoon.
He told Liverpoolfc.com: "Before the game, [the boss] said we have to [show] our quality and be angry because every game is important.
"After the City game, you have to concentrate more because you usually know how it [can go].
"He tried to motivate us like usually and, in the end, everybody was in the right place at the right time to win every ball.
"We played well today and created many chances, scored three goals and it was well deserved."
Mane was joined on the scoresheet by fellow forwards Mohamed Salah and Roberto Firmino - the seventh time this season all three have netted in the same game.
Reflecting on Salah's 40th goal of a remarkable debut campaign, Mane added: "Incredible. He is doing a very good job for us, always scoring.
"We are very happy to have Mo and we are going to help him score more goals. Bobby also scored and I'm happy for him as well.
"But always, the three points is the most important thing.
"I always enjoy playing alongside these great players and if you play with these kinds of players it's always easy to understand each other.
"They make everything easier."
The second leg against Manchester City marked the end of a run of three games in just six days for Klopp's men, but they now have a seven-day break before facing West Bromwich Albion.
Mane continued: "It was not an easy week for us because it was too close to play each game but as professionals we tried to do it and everything [went] well.
"Now we have another week's rest so we are going to go and rest well and come back as strong as we can."