The Rome club won 4-1, but Ballardini was unhappy with several of his players, particularly Zarate.
The coach said: "Zarate was the penalty taker, but he didn't deserve to take it, because he had an ugly game. But this is not the problem.
"On the whole, Zarate did not do well in wanting to be alive in the play, with or without the ball. Zarate could have done a lot more. Today he had an enormous score for losing the ball. He is a great player if he is in the game. As for quality, he remains one of those players who can invent something in any given moment.
"But management is not only about teaching technique. It also means education, respect for your team-mates, professionalism. This is what I am talking about."
"There was an attitude that bothered me a lot. In the week of the game against Inter, Zarate left for Argentina and returned to Rome only on December 29, late and without permission. You can make mistakes but you also have to reflect on your errors.
"It's a management problem, the club didn't give him any permission. I look at attitude. This behaviour is not right towards his team-mates, those people with whom he trains, but also the fans who like to see Zarate.
"I have not said that it's Rome's fault. It's the atmosphere that leads you into having these tensions, this attitude, the desire to be a protagonist. For me, it's the team that has to be the protagonist. Rome can lead you to being too individualistic."