David Petraeus said at the University of Southern California military event his actions had caused “pain for family and friends”.
But the retired general said he hoped his fall would teach others that “life doesn’t stop with such a mistake and must go on”.
David Petraeus quit after his affair with biographer Paula Broadwell was discovered during an FBI investigation.
He was speaking to about 600 guests at the University of Southern California’s annual Reserve Officers’ Training Corps dinner.
David Petraeus received a standing ovation, then began his speech by saying: “Needless to say, I join you keenly aware that I am regarded in a different light now than I was a year ago.”
The former CIA chief said he was also “keenly aware that the reason for my recent journey was my own doing”.
David Petraeus added: “So please allow me to begin my remarks this evening by reiterating how deeply I regret – and apologize for – the circumstances that led me to resign from the CIA and caused such pain for my family, friends and supporters.”
David Petraeus has kept a low profile since resigning on November 9, 2012.
His lawyer said David Petraeus had spent much of the time with his family.
A harassment complaint by Florida socialite Jill Kelley over emails she had received had led the FBI to unmask the affair.
Jill Kelley knew David Petraeus through social contacts on the Florida military base where US Central Command is headquartered.
When the FBI investigated, it traced the emails to an apparently jealous Paula Broadwell.
Jill Kelley also knew the top US general in Afghanistan, General John Allen. John Allen also sent emails to Jill Kelley but has been cleared of any misconduct.
Towards the end of his speech, David Petraeus said he hoped his experience “can be instructive to others who stumble or indeed fall as far as I did. One learns, after all, that life doesn’t stop with such a mistake. It can and must go on”.
David Petraeus added: “I know that I can never fully assuage the pain that I inflicted on those closest to me and on a number of others.
“I can, however, try to move forward in a manner that is consistent to 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.”
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