Despite four points from the last two games, Gilardino was sacked and replaced by Patrick Vieira this week.
Preziosi told TMW Radio: "I believe that a change of coach presupposes that there is a strategy behind it from the club, perhaps a change at a strategic level.
"A coach who has made four points in the last two games cannot be fired. Last year he had a more complete team with different values. Gilardino's value was exceptional. Everyone was surprised, as an outsider there is something that doesn't add up.
"What do I say to the fans? I don't say anything, I haven't spoken about Genoa for three years, but I believe that this club, for those who control it, is solid, and I'm not talking about 777. If a new shareholder comes in I believe he can secure everything.
"(Patrick) Vieira? They have made different assessments, it's a risk but they are convinced that he is the man of providence and let's hope it's like that.
"(Mario) Balotelli? I have seen him change as a person, I would have trusted him but I wouldn't have taken him for Genoa at this moment. He has great qualities but he needs time to settle in, even on a physical level."