Simeone responded by confronting Liverpool supporters close to the away technical area, before receiving a red card from the official and being forced to observe the closing stages from the stands.
Previously, the Atletico boss and his squad had celebrated exuberantly in front of Liverpool fans following a deflected strike that saw the Spanish side level at 2-2, despite trailing by two goals early in the encounter.
Simeone, 55, justified his loss of composure during his post-match media briefing, claiming that he had been "insulted". He said: "They always talk about taking care of each other, but they insult you throughout the entire match and you can't say anything because you're the manager."
"My reaction was unjustifiable, but do you know what it's like to be insulted for 90 minutes, to turn around after the opponent scores and still be insulted? It's not that easy.
For the latest breaking stories and headlines, sign up to our Daily Express LFC newsletter.
"[The referee told me] he understood me. I hope Liverpool can improve that aspect and that when they identify the person who did that, there will be consequences.
"There were insults throughout the match, including gestures. It's clear that I'm the one who has to stay calm, I have to put up with the insults, the gestures and any situation. Because I'm in a position where I have to put up with it.
"I'm not really going to get into the exact nature of the insults. I don't want to get involved in that. I have got to stay in my place, I know what went on behind the manager's bench. I can't solve society's problem in one press conference. I have to live with it as it exists all over the place all of the time."
Posting a video of the incident on X, the Liverpool supporter who wound up Simeone - identified as Jonny Poulter - cheekily asked: "Do I get the assist?"
Atletico clawed one back to 2-1 just before half-time through Marcos Llorente, although there were suggestions that the goal should have been ruled out for offside. With nine minutes remaining, Atletico completed their comeback when Llorente scored his second goal thanks to another deflection.
However, the drama didn't end there as Van Dijk headed home from a corner in the 92nd minute.