Former CIA chief David Petraeus apologized Tuesday for the "mistake" that triggered his resignation last year, in his first public speech since quitting due to an extramarital affair. Addressing a military audience in Los Angeles, the four-star general voiced regret for the "pain" caused by his relationship with his biographer Paula Broadwell, pledging to try to "make amends to those I have hurt and let down." "I join you keenly aware that I am regarded in a different light now than I was a year ago," Petraeus told over 600 veterans and Reserve Officers' Training Corps students hosted by the University of Southern California (USC). "I am also keenly aware that the reason for my recent journey was my own doing," said the former head of the Central Intelligence Agency and top US general who spearheaded the "surge" in Iraq. "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 my resignation from the CIA and caused such pain for my family, friends and supporters," he said at the event held at a downtown LA hotel. Petraeus, America's most celebrated military leader in a generation, stepped down on November 9 as head of the CIA after admitting to an affair with Broadwell, a counter-terrorism expert and lieutenant-colonel. The FBI stumbled upon the affair when Jill Kelley, a Florida socialite and friend of the Petraeus family, asked investigators to look into threatening emails that turned out to be from an apparently jealous Broadwell. The probe that revealed Petraeus' affair also uncovered potentially "inappropriate" emails between Kelley and the top commander in Afghanistan, General John Allen, although he was later cleared of any wrongdoing. In the wake of the scandal, Petraeus has kept a low profile over the last five months. He has received offers from the financial community and to give paid speeches, been asked to serve as a consultant to major companies and is exploring positions in academia, according to The New York Times. In his speech Tuesday, the ex CIA chief -- who was given a standing ovation at the start and end of his remarks -- called for greater efforts to help returning veterans transition to civilian life. His 25-minute address was also peppered with jokes: at one point he said he been briefed, before coming to the LA event, on the rivalry between USC students and those from the University of California, Los Angeles (UCLA). "I used to do intelligence," quipped the former head of America's national spy agency. Towards the end he returned to his personal downfall, thanking those who had given encouragement to him and his family, saying: "This has obviously been a very difficult episode for us." "But perhaps my 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." He 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." "And that is what I will strive to do," he said.