Díaz thought he had put Liverpool in front in the 34th minute of their 2-1 defeat at Spurs on Saturday, only for the flag to go up for offside.
The VAR ref, Darren England, incorrectly thought the on-field decision was "goal." While he quickly identified that Díaz was onside, he told the referee "check complete" -- which mistakenly told the on-field team the offside flag was correct.
The audio was released in full on the Premier League website, along with a full account of what went wrong and a lengthy statement from the Professional Game Match Officials Limited (PGMOL) after a thorough review was completed.
Speaking in his news conference on Wednesday, Klopp said the right thing to do would be to replay the clash at the Tottenham Hotspur Stadium.
"The audio didn't change it at all, because I was not interested in why things happened," he said. "I saw the outcome, I saw a goal. We scored and it didn't count. So I was not waiting for the audio and sitting there and hoping I find out how it could happen.
"It's really important that, as big as football is, we really deal with it in a proper way. That all of the people involved -- [the] on-field ref, linesman, fourth official and, especially now in this case, VAR -- they didn't do that on purpose. We should not forget that. It was an obvious mistake.
Jurgen Klopp believes Liverpool's match vs. Spurs should be replayed after Luis Diaz's goal was incorrectly disallowed.
"Not as a manager of Liverpool so much, more as a football person, I think the only outcome should be a replay. Probably will not happen. The argument against that will probably be that if we open that gate then everyone will ask for it.
"I think the situation is that unprecedented that... something like that, as far as I can remember, never happened. That's why a replay would be the right thing."
England and his assistant Dan Cook were replaced for their next matches -- Nottingham Forest vs. Brentford and Monday's Fulham vs. Chelsea game -- and neither have been listed as officials for any of this coming weekend's Premier League fixtures.
Klopp added: "I'm not angry with any of them, not at all. We should not go for them. They made a mistake, and I'm sure they felt horrible that night."
"I stick to the opinion that it is not a red card," he said. "The ref got called to the screen and saw for the first three seconds a frozen picture. I would give immediately a red card for that picture.
"Then he sees the replay in slow motion and I would have given a red card for the slow motion, but in real time it is not a red card."
Diogo Jota was the other Liverpool player sent off after picking up two yellow cards in quick succession.
Liverpool face Belgian side Union Saint-Gilloise at Anfield on Thursday in their second Europa League match after beating LASK Linz in their opening match.
Information from Reuters was included in this report.