Losing 1-0 in the same tie, same venue last season, the Reds were poised on gaining a point from such a crunchy fixture but late errors saw Napoli maintain their bragging rights at home soil over the Premier League giants.
And with many seeing the loss as a factor to frustrate their goals for the new season, Van Dijk has insisted they need not to be nervous but be firmed on their objectives for the season.
"I don't know if it's a wake-up call," the star defender told UK newspapers.
"Both sides were full in the game and thought it was going to be a draw. Obviously the penalty changed it all and we're going home with no points but it shouldn't be a wake-up call.
"We've been performing since the start of the season outstanding so there's no reason for panic. The majority in the game we played well, we put them under pressure and we created opportunities on the break.
"There's a lot of positive things apart from the result. We have to try to win our other games and we now focus on Chelsea."
Having urged the side to overcome their loss at the Stadio San Paolo and focus on their next games, the Dutch defender also stressed Liverpool were on the verge of securing a point from the fixture before they gave away a penalty to put Napoli in front.
"It happens, it's football. Things happen like that. Sometimes you wish in the end something different, or you pick the other pass instead of the right pass. It's always like that sometimes," he said.
"We had moments in the game we could've done better. If the penalty wasn't there I think it was going to be a draw. The reality is we conceded the penalty and unlucky that Adrian is unable to save it."
Liverpool will look to extend their winning ways in the Premier League with a game against Frank Lampard's Chelsea on Sunday.
