Klopp oversaw an unforgettable night at Anfield, where last season's runners-up Liverpool sensationally overturned a 3-0 first-leg deficit in a 4-0 victory over Barcelona to progress to the final.
Braces from Divock Origi and substitute Georginio Wijnaldum saw Liverpool complete the great escape as their incredible season reached new heights on Merseyside.
And Liverpool are one point behind leaders Manchester City heading into the final match of the Premier League season, despite boasting 94 points and just one defeat in 37 games.
Klopp has endeared himself to the city and club and former midfielder Johnston – who won five league titles and the European Cup in a seven-year spell with Liverpool during their dominant years in the 1980s – compared the charismatic German to former manager Shankly.
Shankly won 10 trophies during his time in charge, including three league titles and the UEFA Cup.
Speaking to Omnisport, Johnston said: "I was at the club for a long, long time and the name Bill Shankly would always come up. There'd always be a story from the old guys there like Tommy Smith. Having seen dozens of managers come through, two words come to mind… Jurgen Klopp.
"You're mentioning him in the same breath as Bill Shankly. You don't have to say much more. When talking about Klopp, I think heart, love, desire, passion, knowledge, craft, team spirit, fantasy because he has a touch of the fantasist about him and so do the Scousers. He has a sense of humour. He's genuinely funny. He recognises the Scousers like Shankly did. He wasn't a Scouser."
Former Borussia Dortmund manager Klopp has awoken Liverpool since arriving in 2015, establishing the Reds among Europe's elite.
Liverpool have reached the Champions League, Europa League and EFL Cup finals under his management, while they are within a whisker of Premier League glory and their first league crown since 1990.
Klopp, however, is yet to taste silverware with the club. But Australian Johnston still regards the 51-year-old as a Liverpool legend.
Asked if Klopp is already a legend at Liverpool, Johnston replied: "Yes, because I think they've overperformed. If I had to say something else, if you look at Manchester City's team, they've underperformed.
"When you think about the stars on the field [against] Barca last night… Jordan Henderson was man of the match for me. That's guts. He was a star and held it together.
"Is Jurgen a legend? Absolutely. Even if they don't win anything, God forbid that won't happen. They've won so much, imagine all the hearts around the world won last night. Real Madrid will love us now. He's an absolute legend."
It was another famous night for Liverpool – who rallied from 3-0 down to beat AC Milan in the 2005 Champions League final – at Anfield, just like in 2004 against Olympiacos and 2016 versus Dortmund in the Europa League quarter-finals – the stadium bouncing as thousands of fans produced a spine-tingling rendition of 'You'll Never Walk Alone'.
"What you have to understand is this is a very unique city with unique people," Johnston said. "They're not Mancunians, Londoners or Geordies. They have this really romantic vision of life sometimes and ironic sense of humour. They're different and incredibly hopeful and they always punch above their weight.
"I haven't seen it in too many other cities like it is in Liverpool. Firstly, it's the people and then you have a fortress like Anfield and that's what it is. Bill Shankly said 'I'm going to build a fortress' and 'give me an army full of Scousers and I'll build you a team to beat the bloody world'.
"So you have the history, the people and the fortress. You have history and track record of winning and turning things around. It's David v Goliath and whenever Liverpool are the little guys, they come up big.
"If you look at the Liverpool team without [Mohamed] Salah and [Roberto] Firmino and you'd said before the game, 'How many would get into the Barcelona team?' You'd go 'I don't know'. After the game, you'd say all of them.
"The funny thing in our day when we were winning everything, Manchester United had the best players and stars, we had [Kenny] Dalglish, [Ian] Rush, [Graeme] Souness and [Alan] Hansen down the middle. But we had a lot of grafters, like last night. That was a grafter's performance against Barcelona. It created an energy that even Barca just went 'oh my goodness' and got a touch of the scaredy pants half way through and started to make mistakes.
"The other thing is Barca actually played well. That's the remarkable thing for me is they played incredibly well. That just shows you how good Liverpool were."