Friday night's 2-0 defeat to Milan was halted for nine minutes when tear gas floated into the arena. It emerged a group of Genoa ultras were waiting for a bus of Rossoneri supporters so they could pelt it with rocks and fireworks.
"Last night's incidents are absolutely to be condemned. Unfortunately, in every fanbase there is a small fringe group who create these dangerous situations," said President Preziosi.
"We must discourage them with tougher laws and punishment."
The Stadio Luigi Ferraris, nicknamed Marassi, has long been a particularly dangerous arena because it is surrounded by a maze of narrow side-streets.
"Our stadium is wonderful, but clearly when these things happen, it is more difficult for the police to guarantee public safety because the arena is right in the city. In future we will evaluate the project for a new stadium."