The Argentina international scored in the final seconds of the match to secure victory for the Premier League side.
Claims from Villarreal have come to light accusing the 23-year-old of boasting about the City win once the contest was over.
"What he has done doesn't say much about the guy," ESPN quotes Villarreal president Jose Manuel Llaneza as saying.
"I think it's a lack of respect, ethics and team spirit. I thought he had learned better. I don't understand why he would mock fellow players for losing."
Villarreal defender Carlos Marchena also criticised the former Atletico Madrid star. "In football you have to have class, especially in times like this," he said. "What Aguero did is not acceptable. These situations are a shame and are a mark of the man who does it."
The City frontman was forced to deny the allegations via his personal Twitter account, stating: "I have no interest in getting involved in controversies, but I have to deny having mocked a Villareal player.
"Everyone can attest to my discipline and professionalism, I wouldn't do something like that."
The Premier League side have not commented on the alleged incident.