Liverpool were denied a perfect goal scored by Luis Diaz at a time when they were down to ten men and ended up losing 2-1 courtesy a last-minute own goal by Joel Matip.
The Premier League's referees body, PGMOL, admitted it erred in disallowing the goal and on Tuesday released audio recordings from the VAR room that transpired in that moment.
Klopp said: "It's really important that as big as football is and important as football is we deal with it in a proper way.
"All the people involved, the on-field referee, linesman, fourth official and especially in this case VAR, didn't do that on purpose. It was an obvious mistake and I think there would have been solutions for it afterwards.
"Some people probably don't want me to say, but not as the manager of Liverpool so much, more as a football person, the only outcome should be a replay. That's how it is. It probably will not happen."
Klopp added: "The argument against [a replay] will probably be if we open that gate then everybody will ask for it. The situation is so unprecedented that I'm 56 years old and I'm absolutely used to wrong decisions, difficult decisions but something like that as far as I can remember never happened.
"That's why I think a replay would be the right thing. If it happened again, a replay would be the right thing to do or the referee has the opportunity to bring both coaches together and say, 'Sorry we made a mistake but we can solve it. Let Liverpool score a goal and we can start from there.'
"I'm not angry with anybody, not at all. We should not go for them. They made a mistake and they felt horrible that night, I'm 100 per cent sure. That's enough for me, nobody needs further punishment."
Liverpool's defeat was their first in the Premier League this season.
