The Spaniard guided the club to a famous penalty shoot-out win over AC Milan in 2005 after they trailed 3-0 at half-time.
This season, the Reds will look to emulate that success when they take on Real Madrid in Saturday's final and the memories of that night in Istanbul have been brought up again 13 years later.
And Benitez feels the period had a huge effect on him, suggesting replicating it will change a lot for Klopp, too.
"But to come to England and win the Champions League with a different team was massive.
"Maybe it will change everything for [Jurgen] Klopp in Liverpool. He's fine. He's an idol now, but he will be more than that."
Benitez is still lauded by Liverpool fans for his success, but believes the current squad are stronger than the team he won the competition with.
"I think this one is better," he said. "We achieved what we achieved – we talk about the 'Miracle of Istanbul', but this team is better.
"We had Stevie [Gerrard], of course, also some players with experience and quality, [Xabi] Alonso and [Dietmar] Hamann. We had players who worked hard; we had a very good balance.
"This team also has good balance, but the front three can make a difference on their own."
Liverpool's run to the final in 2017-18 has thrilled many and Benitez insists they could go one step further and lift the trophy again.
"The difference between the Premier League and the other leagues is the intensity of the games," he said.
"Liverpool and their offensive players, their midfield and their defence have the intensity to hurt you if they do it well.
"Real Madrid has the experience and the quality to match them, but Liverpool can do it. They have the energy, the passion and the desire."