The Daily Mail says Aguero upset his opponents following his last-gasp winner at the Etihad Stadium.
Villarreal vice-president Jose Manuel Llaneza and defender Carlos Marchena criticised the former Atletico Madrid striker after players from both teams exchanged insults in the tunnel at the end of the game.
It is understood that Aguero was heard singing a song in Spanish as he left the pitch and that this could be what has upset Villarreal.
Marchena, who scored an own goal in the first half on Tuesday, said: "In football you have to have class, especially in moments like this.
"What Aguero did is not worthy and especially how he did it. These situations are a shame and they tell you about the person who does them.
"You have to be a good person as well as a good sportsman, and show class which he hasn't got."