Petraeus, the U.S. Army general who led coalition forces in Iraq and Afghanistan, has maintained a low profile since he resigned the directorship after admitting to an extramarital affair with his biographer, Paula Broadwell, in November.
Petraeus told about 600 guests at Tuesday's event honoring veterans and ROTC students at the University of Southern California he is "regarded in a different light now" than he was a year ago, the Los Angeles times reported.
"I am also keenly aware that the reason for my recent journey was my own doing," he said. "So please allow me to begin my remarks this evening by reiterating how deeply I regret -- and apologize for -- the circumstances that led to my resignation from the CIA and caused such pain for my family, friends and supporters."
Petraeus, 60, considered the architect of the U.S. military's counterinsurgency doctrine, also said he wants to move forward, the Times said.
"One learns after all that life doesn't stop with such a mistake," he said, "it can and must go on."
Before his speech, Petraeus generally stayed out of the public eye.
"I know that I can never fully assuage the pain that I inflicted on those closest to me and on a number of others," Petraeus said Tuesday. "I can, however, try to move forward in a manner that is consistent with the values to which I subscribed before slipping my moorings and, as best as possible, to make amends to those I have hurt and let down."
One friend told the Times Tuesday, "I don't think it's in his DNA to just retire."
Petraeus has been mum about his plans, except to say he agreed to support several non-profit organizations that assist veterans.
Petraeus received two standing ovations during his speech in which he said the nation has a responsibility to look after families of fallen soldiers, care for the wounded, help veterans move into to civilian life and honor their service.
"We can and must do more," he said. "Helping those who have given so much is simply the right thing to do."