In the second part of an interview with Oprah Winfrey, aired on Saturday, Armstrong said the foundation was "like my sixth child".
Livestrong is said to have raised $US500 million since its inception in 1997.
- Armstrong apologised to his fans, telling them he would do anything he could to earn back their respect.
- He fought back tears as he described how his son Luke defended him at school.
- Armstrong says he took a financial hit of $US75 million as his sponsors left him.
- He says he received the sporting equivalent of a "death penalty", but he deserves to be punished.
- Armstrong admitted to doping in the first instalment of the interview. Read the story.
Armstrong admitted in the first part of the interview that he was driven by the "mythic, perfect story" of his fightback from cancer as he inspired millions around the world.
He told Oprah that his departure from the charity was more difficult than being exposed for doping and being stripped of his titles.
"That was the most humbling moment - to get that call to stand down as chairman," he said.
"I wasn't forced out - told to leave - I was aware of the pressure.
"It was the best thing for the organisation but it hurt like hell."
'Don't defend me anymore'
Armstrong fought back tears as he described how the cheating scandal had affected his family.
He said one of the chief reasons he confessed to doping was for his children.
"The older kids need to not be living with this issue in their lives. That isn't fair for me to have done to them. And I did it," he said.
"And also for the little ones who have no idea - they're two and three. They obviously have no idea but they will learn it. This conversation will live forever."
Armstrong described how his son Luke would defend him when children at school called him a cheat.
"I saw my son defending me, saying 'That's not true - what you're saying about my dad is not true'," he said.
"I said Luke, 'Don't defend me anymore - don't'."
Armstrong addressed his fans, saying he understood their anger and he would do all he could to earn back their respect.
"I understand your anger, your sense of betrayal. You supported me forever throughout all of this and I lied to you and I am sorry," he said.
"I am committed to spend as long as I have to to make amends."
Armstrong said that he wanted to compete again, but the lifetime ban handed down by the United States Anti-Doping Agency (USADA) is the equivalent of a "death penalty".
He said that he deserved to be punished for his actions but he did not deserve the sanctions imposed, particularly in light of those handed down to other self-confessed drug cheats.
"I am not saying that's unfair - I'm saying it is different," he said.
"I deserve to be punished but I am not sure I deserve the death penalty.
"With this penalty, this punishment, I made my bed.
"Would I love to run the Chicago marathon when I am 50? I would love to do that but I can't."
Armstrong said he took a $75 million hit when his sponsors left him after last year's damning report from USADA.
"You asked me the cost - I don't like thinking about it but that was a $75 million day. Gone," he said.
'Don't cross that line'
In the first instalment of the interview on Friday, Armstrong admitted to doping during his seven Tour de France victories between 1999 and 2005, confirming that he used EPO, human growth hormone, and testosterone.
However, the disgraced cyclist said he did not cheat during after his final Tour victory in 2005 - a statement immediately dismissed by the president of the World Anti-Doping Agency (WADA).
In today's interview, he said one of the conditions of his return to cycling in 2009 was that he did not blood dope.
He said his ex-wife Kristen gave him her blessing to returning to competitive cycling on the condition that he "never crossed that line again".
"And I never want to betray that with her. It's a serious ask - it was a serious moment," he said.
"If she had said, 'No, I don't like this idea', I would not have done it."
WADA chief John Fahey told Britain's Daily Telegraph after the first instalment of the interview yesterday that blood evidence from the USADA shows "with absolute certainty" that Armstrong doped during his comeback.
Fahey said Armstrong may not have been able to confess in full due to legal ramifications.
"The evidence from USADA is that Armstrong's blood tests show variations in his blood that show with absolute certainty he was doping after 2005," he said.
"It struck me that the statute of limitations under US law might be relevant and Armstrong would not want to admit to anything in regards to his comeback that might be picked up under the US criminal code."
Australian cyclist Robby McEwan told ABC Radio this morning he will never forgive Armstrong.
McEwan won two of his three Tour de France green jerseys for best sprinter during Armstrong's era of dominance.
"Not only bike riders, but the fans, the press - everybody wanted to believe this beautiful story," he said.