At a news conference in State College, Corbett also expressed disappointment in Paterno and university President Graham Spanier, who were fired by university trustees the night before for their handling of child sex abuse allegations against a former assistant football coach.
Thousands of students took to the streets Wednesday night after Paterno's dismissal, overturning a TV news van and throwing rocks, bottles and other hard objects at police and others.
"I believe in your right of assembly and your right to express your opinions," Corbett said. "I do not believe, nor does anyone believe, in your right to violence."
Investigators said they were reviewing video footage and have identified numerous suspects who could be charged with riot, attempted arson or other counts.
"The crowd initially was a peaceful demonstration against Coach Paterno's firing. The crowd quickly turned from a peaceful demonstration to a riotous mob," State College police said in a statement. "The mob attempted to light vehicles on fire, and tore down light posts and street signs."
In the statement, police estimated the crowd totaled as many as 4,000 to 5,000 people and that officers made numerous orders to disperse but eventually had to use pepper spray. About 100 police officers were downtown, many wearing helmets.
Authorities didn't say how many arrests had been made.
Paterno had announced earlier Wednesday that he planned to retire after the season and expressed remorse for not having done more after he learned of sex abuse allegations that had been lodged against former defensive coordinator Jerry Sandusky, who has denied the charges. On Wednesday night, the board of trustees announced his immediate firing.
Meanwhile, a group that advocates for the rights of people abused by Catholic priests released a statement cautioning Paterno's supporters to think about the consequences of their actions.
"As for the students who are rallying around Paterno, we hope university officials will ask them to consider the anguish their actions are causing the victimized children as well as other members of their community who are victims of sexual violence," BishopAccountability.org said in the statement.
"To observers of the Catholic crisis, this phenomenon is sadly familiar," the group said. "The students are similar to the parishioners who rally around abusive priests and complicit bishops. This kind of deference to powerful authority figures helps create a culture in which victims are silenced and officials feel entitled to hide crimes rather than calling the police. "