The German manager's last trophy came in 2014 when he won the DFL Supercup with Borussia Dortmund, while he narrowly missed out on guiding Liverpool to the Europa League, League Cup and Champions League in subsequent years.
Having finished as runners-up in all three competitions under Klopp, the Reds finally claimed silverware under his stewardship when they beat Tottenham 2-0 in Madrid to clinch Europe's top prize for the sixth time.
Klopp expressed his relief at having ended his drought and said the memory of the celebrations in Liverpool city centre would spur his players on in 2019-20.
"It was actually better than I expected, to be honest, because it was long ago that I won something so I didn't know exactly how it feels anymore," Klopp told Liverpool's official website.
"Of course we move on. It's not that wherever we go it's like, 'Morning, we won the Champions League!'. But why should we forget it?
"It's just something that should give the boys more confidence – that's important. But if you only use confidence you have no chance, but nobody should worry about this team.
"It's not about being finally satisfied, happy or done with our careers because we won the Champions League, there is so much to go for.
"We smelled really how it feels – we played the final, we won the final, we came into the city, we saw the city and saw the people. That’s something you can get addicted to, you want to have that much more often."
Klopp's contract at Anfield expires in three years and his agent, Marc Kosicke, said the club's directors are keen to tie the 52-year-old to a longer deal.
In addition, Kosicke pointed out that Germany coach Joachim Low is also on a contract that runs out in 2022 and indicated that taking charge of Die Mannschaft is not out of the question for his client.
"Jurgen himself once said that in the event that Jogi Low someday no longer wants to be a national coach and the role became available, this is an option for him," Kosicke told Die Welt.
However, Kosicke added that Klopp is in no mood to think about leaving anytime soon, saying: "He felt again, at the recent city festivities, what a great club Liverpool is and that he is in the right place at the right time."