VAR failed to overturn an incorrect decision to disallow a Luis Diaz goal for offside with the match goalless.
In a statement on Sunday, the club said they will “explore the range of options available given the clear need for escalation and resolution”.
The VAR officials were stood down from duty for the rest of the weekend.
PGMOL, the governing body for referees, has said the decision to disallow the goal was “a significant human error”.
Liverpool say that explanation is “unacceptable” and called for a “review with full transparency”.
PGMOL admitted that VAR official Darren England and assistant Dan Cook failed to act after Diaz’s 34th-minute strike at Tottenham was wrongly ruled out for offside.
Still images of the incident showed Tottenham defender Cristian Romero playing Diaz onside.
The disallowed goal came when the match was level but with the Reds down to 10 men after Curtis Jones had been controversially sent off following England’s intervention.
BBC Sport understands the correct procedure was followed for the offside decision but the mistake was down to human error.
The lines were drawn in accordance with normal procedure and every other aspect was checked.
However, what is being described by sources as a lapse of concentration led to a loss of focus around the initial on-field decision and then a ‘check complete’ being confirmed rather than an intervention that would have resulted in the goal being awarded.
It is understood that referees’ chief Howard Webb has spoken to Liverpool about the incident.
In a statement the PGMOL added: “The goal by Luis Diaz was disallowed for offside by the on-field team of match officials. This was a clear and obvious factual error and should have resulted in the goal being awarded through VAR intervention. However, the VAR failed to intervene.”
Speaking after the match, Liverpool boss Jurgen Klopp said his side’s defeat came in “the most unfair circumstances” with “crazy decisions”.
Klopp also said the PGMOL statement “doesn’t help” and referenced the apology Wolves received for the decision not to award a penalty at Manchester United earlier in the season.
England was replaced as the fourth official for Sunday’s Premier League game between Nottingham Forest and Brentford, while Cook was replaced as assistant referee for the game between Fulham and Chelsea on Monday.
Liverpool then published a statement later on Sunday saying: “Liverpool acknowledges PGMOL’s admission of their failures last night. It is clear that the correct application of the laws of the game did not occur, resulting in sporting integrity being undermined.
“We fully accept the pressures that match officials work under but these pressures are supposed to be alleviated, not exacerbated, by the existence and implementation of VAR.
“It is therefore unsatisfactory that sufficient time was not afforded to allow the correct decision to be made and that there was no subsequent intervention.
“That such failings have already been categorised as ‘significant human error’ is also unacceptable. Any and all outcomes should be established only by the review and with full transparency.
“This is vital for the reliability of future decision making as it applies to all clubs with learnings being used to make improvements to processes in order to ensure this kind of situation cannot occur again.
“In the meantime, we will explore the range of options available, given the clear need for escalation and resolution.”