A Mohamed Salah penalty and Divock Origi strike saw Liverpool overcome Tottenham 2-0 in the decider in Madrid on Sunday (AEST).
After helping the Premier League giant win a sixth European crown, Mane, who has been linked with Real Madrid, said the squad would push on.
"We have more things to come," he said.
"We will do everything to win [more] trophies with this squad."
The star attacker added: "We are very proud and very happy to win this trophy. The dream has come true.
"I could not have anything better."
Mane produced a good display in the final, but Liverpool needed some fine stops from goalkeeper Alisson to secure the win.
The Senegal international believes Brazil shot-stopper Alisson deserves to be recognised as the world's best.
"I can't describe how good Alisson was — I saw him make incredible saves for us," Mane said.
"We are very happy to have him in our squad. He makes us even better. For me he is the best in the world."