His side was losing 4-0 at the 53rd minute when ultras staged a protest that involved throwing fireworks on to the pitch, climbing on top of the tunnel and demanding the players remove the jerseys they were "unworthy" to wear.
"The fans must understand that their behaviour affects the performance of the team. If we had not finished the match, then we could've had points docked," said Preziosi, who was also in the stadium.
"It is a great shame that 60-100 people can act with impunity and do whatever they want without being checked. We have no sporting culture here, as people must learn to accept defeat.
"I have made many mistakes in my time here, but I cannot go under the Curva Nord every game to apologise personally.
"In fact, I hope we will be banned from playing on home turf, that way we can play in a calmer atmosphere. I cannot stand for behaviour like this, nor can the true Genoa fans. It's just not right.
"However, I will not give up. We have to believe in our chances. I have to reflect on some issues."