Liverpool say "sporting integrity has been undermined" by the video assistant referee (VAR) error in Saturday's 2-1 Premier League loss to Tottenham.
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".