Corbett, who is on the 32-member board along with 10 gubernatorial appointees, made the comments after a second day of private meetings of Penn State trustees amid an unfolding child sex abuse scandal involving the university.
Asked if he thought that Paterno and Spanier didn't do enough to alert law enforcement to protect the safety of children, Corbett said he was disappointed in their actions.
"I support the board's decision," Corbett said. "Their actions caused me to not have confidence in their ability to continue to lead."
Corbett, the state's former attorney general, wouldn't answer questions from reporters about any of the board's internal discussions in the wake of a grand jury report released Saturday that said former football assistant coach Jerry Sandusky had sexually assaulted multiple boys, including some on university property. Sandusky has denied the allegations.
The trustees announced Wednesday night that Paterno, in his 46th season coaching Penn State's storied football team, would no longer be coach and that Spanier would no longer be president.
"Certainly every Pennsylvanian who has any knowledge of this case, who has read the grand jury report, feels a sense of regret and a sorrow to also see careers end," Corbett said. "But we must keep in mind that when it comes to the safety of children, there can be no margin of error, no hesitation to act."
Scrutiny fell on Paterno and Spanier after the grand jury report said a team graduate assistant was in the locker room on the night of March 1, 2002, when he discovered what he said was a naked boy being sexually abused by Sandusky.
Paterno and Spanier have said they weren't told the exact details of the incident or the seriousness of the matter, but state police Commissioner Frank Noonan has suggested that they fell short of their moral responsibility to alert police.