The Argentine had seen his side claw back a two-goal deficit but Virgil van Dijk then headed into the net in the 92nd minute to condemn Atletico to a 3-2 defeat at a raucous Anfield.
Simeone appeared enraged by a Liverpool fan behind the technical area and was eventually sent down the tunnel by Italian referee Maurizio Mariani.
Afterwards he said he had endured insults for 90 minutes.
"There have been insults all match, but hey, I'm the one who has to stay calm and endure everything: insults, gestures, etc," he told Movistar. "(Liverpool) been talking about putting on a good show, but they insult you all match from behind and you can't say anything, because I'm the coach.
"My reaction to the insult isn't justifiable, but you don't know what it's like to be insulted for 90 minutes non stop.
"And of course, when the opponent's goal is just around the corner, you turn around and they keep insulting you, and with the tension, what happens is what happens.
"The referee told me he understood, but I hope Liverpool can improve and if they identify who did that, there will be consequences."
Asked later during his press conference what exactly had been said to make him lose his cool, he said: "I'm not really going to get into the exact nature of the insult, I don't want to get in that discussion.
"I've got to stay in my place, I know what went on behind the manager's bench, I can't solve society's problems.
"Never very good when we react as managers, is it? If we get insulted all the game... when they scored the third goal, he insulted me, I turned around again, I'm human."
Simeone praised his team who showed great resilience after conceding twice in the opening six minutes but hit back with a double by Marcos Llorente.
"We were unlucky with the first goal, it threw us off course, but with the spirit and quality of the lads we got back into the match, and with Llorente, who had a great match, we raised our level," he said.
"We had the match on the edge until a great goal from Virgil left us with a bitter taste in our mouths but with spirit."
