Roma triumphed 4-2 on Wednesday at the Stadio Olimpico thanks to a pair of late Radja Nainggolan goals, but Liverpool's stirring 5-2 win at Anfield last week meant a remarkable 7-6 aggregate victory for the Premier League team.
Holders Real Madrid await in a Kiev final later this month and many of the plaudits during Liverpool's incredible run have landed at the feet of lethal front three Mohamed Salah, Sadio Mane and Roberto Firmino.
Mane opened the scoring and impressed throughout in the Italian capital but, when asked whether the Senegal international's showing represented his best in Liverpool colours, Klopp told a post-match news conference that his forwards falling short in other aspects of the game meant goalscorer Georginio Wijnaldum, James Milner and captain Jordan Henderson were left covering "gaps as wide as the [River] Mersey" in midfield.
"No, it wasn't, it wasn’t his best ever for the club," Klopp replied. "Sadio Mane is an exceptional player, unbelievably important.
"Not only Sadio, but Mo, Bobby, the last row… I really think the three midfielders were the best players, they had to close gaps as wide as the Mersey.
"We can play much better, so Sadio – what a game, scored one goal, was really involved in good situations - but all the counter-attacks, we all know Mo, Bobby and Sadio can do it better.
"We were not patient enough. There is enough space for improvement and that’s no problem. We have to improve in the short-term and in the future, and we can. He is a very, very important part of the team. I love this boy and he can do better."
YYEEEEESSSSSSSSSS!!!! Kiev here we come!!! pic.twitter.com/NIVKjLHCiy— Liverpool FC (@LFC) May 2, 2018
Juventus were also close to derailing Madrid's run and are in the process of seeing off a thrilling tilt for the Serie A title from Napoli – leading Klopp to hail a renaissance for Italian football in the months after the country missed out on the 2018 World Cup.
"My biggest compliment to Roma and [head coach] Eusebio Di Francesco - what a job," he added.
"They are a really good football team, [they play] really good football. A lot of people talking about the English league being the best in the world and that's probably right, but what teams [there are] in Italian football at the moment.
"Juventus had Real Madrid at the edge and Roma had us at the edge. It is a really big compliment."