Disgraced cyclist Lance Armstrong hopes for a second act with a new venture capital fund: 'I don't feel like a failure'

Lance Armstrong wants people to take a chance on him again, this time with a new capital venture fund.

But he understands why people may not trust him.

The disgraced cyclist was stripped of his seven consecutive Tour de France titles in 2012 after evidence surfaced he used performance-enhancing drugs. He vehemently denied the charges until an interview with Oprah Winfrey in 2013.

Armstrong won his first Tour de France in 1999 after he recovered from cancer. He became an inspiration to the world about what seemingly could be done in the face of adversity.

"Of course there were lies," Armstrong recently told CNBC's Andrew Ross Sorkin. However, it was the "bullying" that was "terrible," he added. "It was the way I acted, that was my undoing."

Since the scandal, Armstrong has been banned from cycling for life. He also settled with the federal government for $5 million in a whistleblower lawsuit earlier this year and paid over $20 million in damages and settlements in other lawsuits.

Now as his new fund, Next Venture, is reaching out for meetings, Armstrong is finding some people just won't return his calls. "You have to assume that's what they're thinking: 'I don't want this association; I don't trust this guy,'" he said in an interview, which aired on "Squawk Box." "I understand. I'm not going to be upset or bitter about that. You have every right. And quite frankly maybe you should feel that way."

That said, he believes his firm, which invests in sports, fitness, nutrition, and wellness markets, is "uniquely positioned" and will not be fooled on the product side. "This is our world. It's not as if we have to guess. If it is any product, we test it. We make sure that it works," he said.

While acknowledging his past mistakes, Armstrong dismisses any talk that he's a failure. After his doping admission to Winfrey about five years ago, Armstrong saw a tweet from then-businessman Donald Trump.

Lance Armstrong did himself great harm last night. Lawsuits & failure will follow him

Armstrong told CNBC that Trump was right about it costing a lot of money. "[But] I don't feel like a failure. I've never felt like a failure since then." Trump, the onetime real estate mogul and reality television star who would become president, was half right, Armstrong added. "He got a 50."

In fact, Armstrong has already found financial success as an early investor in Uber. In 2009, he invested $100,000 in Chris Sacca's venture capital firm, Lowercase Capital. The bulk of the money went to Uber. That investment has "saved our family," said Armstrong. While he declined to say how much the investment has yielded, he said the number is "too good to be true."