For the second season running, the Reds were on the receiving end of a late sucker punch in Naples, with late goals from Dries Mertens and Fernando Llorente condemning the European champions to a 2-0 defeat at Stadio San Paolo on Tuesday night.
Liverpool have started the Premier League season impressively, winning their opening five fixtures to open up a five-point gap at the top of the table. They travel to Chelsea on Sunday looking to maintain, or extend, that advantage.
Van Dijk, naturally, was disappointed following the loss in Italy, but says there is no reason for panic after one setback.
“It didn’t feel like a wake-up call,” he said. “It felt like it was going to be a draw, and then the penalty changed everything in the game.
“It shouldn’t be a wake-up call. We have been performing outstandingly since the start of the season so there is no reason to panic. And in the game as well, we played well, we put them under pressure, we created opportunities on the break.
“So there were a lot of positive things, the only thing not positive was the result.”
Klopp himself was critical of his side’s decision-making in Naples as, for the second year in a row, the Reds were unable to find a way past Carlo Ancelotti’s well-drilled outfit. In the end, all three of Sadio Mane, Roberto Firmino and Mohamed Salah endured off nights.
“It happens, it’s football, things like that happen sometimes,” said Van Dijk. “You wish in the end there was something different, or the right pass, you know you pick the other pass instead of the right pass.
“But you know it is like that sometimes - there are always some moments in games that could go better.
“But like I say, if the penalty wasn’t there then it was going to be a draw. But the reality is that we conceded the penalty and it was unlucky that Adrian got something on it, but it didn’t stay out.
“[The front three] made a lot of problems for Napoli, and we had a lot of opportunities, we hurt them a lot, a very strong side on their own ground. It can happen though, it’s part of the game.”
Liverpool arrived back on Merseyside on Wednesday afternoon and will step up preparations for the trip to Stamford Bridge on Thursday.
They should be boosted by the return of midfielder Naby Keita, who is set to resume training after missing the last month with a hip injury.
Divock Origi, though, will miss the weekend’s game having suffered a twisted ankle against Newcastle last week.