Armstrong was speaking to the BBC's Dan Roan, who interviewed the disgraced former Tour de France champion at his bike shop in Austin, Texas, for an interview that aired this week.
"I spent a long time trying to build up an organisation to help a lot of people," Armstrong told the BBC, referring to Livestrong. "And I can't lie: It hurts that that has been put away, or almost forgotten, and almost, in some parts of the world, discounted as if it was a sham or PR. It wasn't. That was very real. It meant a lot to me. And the deepest cut was Livestrong saying, 'you need to step away.'"
Livestrong suffered a 34% slump in donations in 2013 after Armstrong admitted doping, Bloomberg reported in September.
Roan then asked, "How much did that hurt?"
"It doesn't get worse than that," Armstrong said, "but we are where we are."
Roan said, "There's no chance of reuniting with them - that's gone forever?"
"Forever is a big word," Armstrong replied. "I'm not going anywhere.
"Listen, if you asked Steve Jobs somewhere between leaving Apple and going back - somewhere right in those NeXT days - he would have said, 'I don't ever care to go back. I'm going to go build the next great thing.' But ultimately he goes back, and the rest is history."
NeXT was the company Jobs founded in 1985 after he was forced out of Apple, which he also founded. NeXT was eventually bought by Apple, in 1996, when Jobs rejoined the company.
"I want to get back to a place where I can help people and effect change," Armstrong said. "If [Livestrong is] there, great, and hopefully so. But if it has to be elsewhere, then I'll find that place.
"The numbers are there, the dollar value is there, the amount of people who were absolutely, directly served is there - more than 3 million people. And it's been disturbing to me to see the change in the organization, to see the drop-off in the organization."
After Jobs died from cancer, on Oct. 5, 2011, Armstrong wrote a post for ESPN in which he called Jobs "forever a world icon." Armstrong, a cancer survivor, said of Jobs:
We had some common bonds. We had the disease. We both never met our birth father. Neither of us had a college degree. We both like to bike a little. And yet we never talked about any of that.
After the US Anti-Doping Agency, or USADA, stripped Armstrong of his seven Tour de France titles, in October 2012, and after he confessed to Oprah Winfrey to having used banned substances, in January 2013, the Lance Armstrong Foundation changed its name to just Livestrong.
In its "Reasoned Decision," USADA said that evidence against Armstrong showed beyond any doubt that his US Postal Service Pro Cycling Team, with Armstrong as its leader, "ran the most sophisticated, professionalized and successful doping program that sport has ever seen."
Also in the BBC interview, Roan asked Armstrong, "When it comes to the doping, would you do it again?"
"If you take me back to 1995, when it was completely and totally pervasive, I'd probably do it again," Armstrong said.
Armstrong's net worth, according to The New York Times, was estimated at $125 million in 2012. In August he said he still believed he won those seven Tours.
Jobs famously called the computer the bicycle of the mind.