Simeone, after Virgil van Dijk's injury-time winner, clashed with a section of Liverpool fans behind the away dugout before eventually being sent off. The Argentine continued trading insults as he was ushered down the players' tunnel.
After the 3-2 defeat, Simeone said: "Firstly I regret the part I played. It's clear we are in a position where we do not have the right to react and it is not good when we react.
"We (coaches) are in a position where we are protagonists/standard bearers, so in the same manner that we fight against racism and insults in stadiums today, we could also fight on behalf of the managers, against the insults we receive throughout the whole game.
"It's not easy to be in the position we are in and receive insults for the whole game. I saw it from far away after the third goal. I saw the third goal go in and I turned, the insults continued, and well, I'm a person."
Asked about the insults, Simeone continued: "The truth is I cannot remember exactly. I don't want to enter into the situation.
"The thing I have is that I have to maintain my position. I need to know how to withstand everything that happens in front of the dugout, and know I cannot fix society. I, and whichever manager, has to live with this because it happens all of the time.
"My reaction isn't justifiable but do you know what it is like to be insulted for 90 minutes? I hope Liverpool can improve that aspect and that when they identify the person who did that, there will be consequences."