Liverpool, however, kept up the pressure and were rewarded when Dutchman Van Dijk grabbed his third goal in his last four appearances in all competitions.
The forward was enormous for Liverpool on the evening, not just bagging two important strikes, but also working tirelessly in attack and defence, as well as keeping possession when his side needed it.
"It's massive, a big step for us", said Klopp.
On the instructions from the manager, the centre-back said: "Obviously be courageous when we have the ball, make sure everyone wants the ball and when we defend, defend all together".
"We all feel that's where this club belongs and we proved it at least a little bit".
"A lot of teams struggle here to get a result, but we still did it".
Okay, they might need to improve against say Barcelona or Juventus but this was a magnificent win for the Reds.
"We knew it was going to be very tough".
"Today we didn't play like in the Bundesliga, of course I don't know why".
"It's the first step to win a game like this".
Although some pointed out that each of the teams are managed by different nationalities - with Argentinian Mauricio Pochettino at Spurs, Norway's Ole Gunnar Solskjaer at United, Germany's Jurgen Klopp at Liverpool, and Spain's Pep Guardiola at City - and not to mention a mass of foreign players in the ranks.
Fabinho also spoke about the fact that half of the clubs who qualified for the quarter finals are English.
"I would've liked to have him at Liverpool [when I was there]".
And fans will hope the omens will show they can go all the way to the final again.