The Reds bought the shot-stopper from Roma last summer for £67 million ($86m) following their defeat to Real Madrid in last year's Champions League final, in which Loris Karius made two decisive errors.
Jurgen Klopp's men redeemed themselves on Saturday when they beat Tottenham 2-0 to claim the European crown for the first time in 14 years and sixth in their history.
Alisson played every minute of Premier League and Champions League football in his debut campaign at Liverpool and his 21 clean sheets in the English top-flight broke a club record for most in a single season.
And the 26-year-old has impressed Achterberg with his role in their journey to continental success, as the coach believes he has proven himself as one of the world's best in his position.
"It is unbelievable the way he stayed calm in the difficult situations and the saves he makes, he takes the team through the pressure moments," Achterberg told Press Association Sport.
"Decision-making you cannot train, you train and try to prepare but what he does is so unbelievable in his first year in the UK.
"Also staying calm under high pressure is not teachable, it is natural. In training, you can prepare what’s going to happen in a game and situations you can train but decision-making, when to come, when to stay, when to be calm and when to play, he showed that’s all him.
"We bought an expensive goalie but he paid it back with the trophy, he had a big hand in it anyway."
He added: "There are always things he can improve but the level he has produced this season is probably one of the best in the world. He showed it.
"He has set a standard for himself and to try to overtake it again because that is the drive you have to create as a player, always to be better."
"That’s football. It’s tough for the one and f**king great for the other, it’s true," he said.
"The staff and the players work their balls off and we have to go again.
"You can’t say anything about the investment from the owners either because that has helped as well. Hopefully we keep it going and try to win the next one."