The revelation comes just days after the Reds believed they had become favourites to sign the highly sought-after Dutch international.
Reports suggested van Dijk had picked Merseyside as his desired destination over Manchester City or Chelsea as he was convinced by manager Jürgen Klopp's vision for the club.
But the two clubs had not discussed any potential transfer and the Saints complained to the Premier League about Liverpool's conduct, claiming they illegally approached van Dijk.
Liverpool's apology now implies that they were indeed guilty of wrongdoing, with Southampton adamant that they received no bid for their club captain and that no permission had been granted for Liverpool to talk to him.
Sky Sports have even suggested that Liverpool were potentially facing further punishment for their approach, though their apology is now regarded as the end of the matter.
Earlier this season, Liverpool were fined £100,000 and banned from signing academy players from English league clubs for two years after being found guilty of tapping up a Stoke City schoolboy.
The statement on Liverpool's official website reads: "Liverpool Football Club would like to put on record our regret over recent media speculation regarding Southampton Football Club and player transfers between the two clubs.
We apologise to the owner, board of directors and fans of Southampton for any misunderstanding regarding Virgil van Dijk.
We respect Southampton's position and can confirm we have ended any interest in the player."
Reds dealt embarrassing transfer blow
Officials from the two clubs are believed to have only spoken for the first time about van Dijk on Wednesday, Southampton having already complained on Tuesday about Liverpool's activity.
They argued to the governing body that Klopp's involvement in the deal represented a rule breach and while more details will emerge in the coming days - the current situation suggests Liverpool were found guilty and did not want to risk any punishment.
The situation is a major PR blow to the club, just days after it was announced that Liverpool were willing to put together any necessary financial package - even one exceeding the world record fee for a defender - to beat their rivals to the signing of van Dijk.
The defender was viewed as a priority signing for Liverpool as they look to strengthen their back-line ahead of next season, when Champions League football will return to Anfield if they can navigate a two-legged qualifier in August.
But they will now need to review other potential targets, with ties between Liverpool and Southampton having been severed.
The Reds had signed five players from the South Coast club since the summer of 2014 alone, with Sadio Mané's £30 million move 12 months ago the latest deal.
Nathaniel Clyne, Adam Lallana, Dejan Lovren and Rickie Lambert are the other players to have swapped Southampton for Liverpool, with the Saints said to have become frustrated at consistently losing key players.
It remains to be seen what this means for the future of van Dijk. Southampton are said to be keen on keeping hold of their prized 25-year-old for at least one more season, having penned him to a six-year deal at St Mary's just last summer.
But other clubs could now rekindle their interest in the player with it clear he will not be joining Liverpool, though Southampton are reportedly keen to push for around £60 million if van Dijk is to be sold.