The Reds thought they had taken the lead at the Tottenham Hotspur Stadium when Diaz was slipped in behind by Mohamed Salah, but the Colombian's strike was flagged for offside by the linesman.
A VAR check from Darren England as his assistant Dan Cook was quickly conducted and a 'check complete' was communicated to referee Simon Hooper, who restarted play with a Spurs free kick with the on-field decision standing.
However, the officials realised Diaz had been in an onside position shortly after the restart but were not able to intervene to correct the error, despite the calls from fourth official Michael Oliver.
The conversation of the VAR check was released on Tuesday after a formal request from Liverpool and includes full audio from the linesman, the VAR and the VAR assistant, who discovers Diaz was in an onside position.
In a statement, the PGMOL said: "As stated shortly after the full-time whistle on Saturday evening, we acknowledged in a statement that a significant human error had occurred during the aforementioned match, which we recognise should have resulted in a goal being awarded through VAR intervention.
"As with all goal situations, the VAR team checked every aspect of the goal. After the on-field officials had disallowed the goal for offside, the checking phase and process started and was carried out correctly by the VAR. The kick-point selection was accurate and the use of a single 2D line on the foot of the second rear-most defender was also correctly positioned.
"The image created showed that Luis Diaz was clearly onside, without the need for the insertion of a second line. In a lapse of concentration and loss of focus in that moment, the VAR lost sight of the on-field decision and he incorrectly communicated “check complete”, therefore inadvertently confirming the on-field decision. He did this without any dialogue with the AVAR (Assistant VAR).
"The match then restarted immediately. After a few seconds, the Replay Operator and then the AVAR queried the check-complete outcome with the VAR and asked him to review the image that had been created, pointing out that the original on-field decision had been offside, but this was not communicated to the on-field team at any point during the match.
"The VAR team then gave consideration as to whether the game could be stopped at that point, however the VAR and AVAR concluded that the VAR protocol within the Laws of the Game would not permit that to happen, and they decided intervention was not possible as play had restarted.
"PGMOL has carried out a review into the circumstances which led to this incorrect outcome and the subsequent learnings will be implemented to mitigate the risk of errors occurring in the future."
VAR officials England and Cook have since been stood down from next week's round of Premier League fixtures while the PGMOL and FA will review their policies for referees to officiate abroad after it was discovered the pair had been in the United Arab Emirates just 48 hours prior to the match.
