After a goalless first leg, Liverpool made the trip to Germany to face the reigning Bundesliga title-holders and five-time European champions, genuine heavyweights in this competition.
The fact they went out at the last-16 stage for only the second time since 2011 said as much about Liverpool as it did about an ageing team in need of significant rebuilding.
“It’s massive, a big step for us,” said Klopp.
“We will see what we can do with it but it’s still fantastic for us that LFC as a club, we really are back for the last games of international top football.
“We all feel that’s where this club belongs and we proved it at least a little bit.
“There are some places in the world where whichever team would struggle. If Barcelona comes here, if Real Madrid comes here, Manchester City, it is not that they expect to win. They know it is a very tough place to come.
“But we kept them as often as possible away from our goal. I don’t know about the statistics, but my impression is that there were not too many difficult situations in and around our box.
“It’s the first step to win a game like this. Playing your best football, free-flowing, is not possible against this team because you cannot use your speed really.
“You have to find different ways. We found that and that makes me feel really proud and happy.
“I really think this club deserves to have awareness again. We have a lot to improve, a lot to learn, but we are back and I like that very much.”
The result ended a run of five successive Champions League defeats—including the final last May—away from Anfield and maintained Klopp’s record of never having lost any of the nine two-legged European ties he has overseen as Liverpool manager in Europe.
And fans will hope the omens will show they can go all the way again.
A goalless draw at home in 1981 in the 1981 European Cup semi-final was followed by a 1-1 draw in Germany, resulting in them beating Real Madrid in Paris in the final.