Konsa was seen arguing with the Villa away support at the final whistle, the defender was wearing the captain's armband in John McGinn's absence.
The Daily Mail says Konsa has not been fined by management, but has been reminded of his responsibilities towards the Villa supporters.
Villa's director of football operations Damian Vidagany said: "We spoke with Ezri and we felt that the emotions were very sensitive on both sides. We spoke with him to try to control his reactions.
"At the same time, I think that (for fans) insult or to have a bad reaction with a player is not something we should consider acceptable.
"So, the club talked to the player and I am sure that the fans also need to understand that the emotions of the players after a defeat are in a sensitive moment.
"Anger was in the stands and in the dressing room, and at that moment, we needed to have calm minds, every one of us, to try to carry on and to get together."