"We need to show material progress over the next few months to establish to our senior lenders that a reorganization of the company is realistic and to avoid a shutdown and liquidation," Lampert said at the retailer's headquarters in Hoffman Estates, Illinois, according to exclusive audio obtained by CNBC.
The retailer filed for bankruptcy Monday, saddled by debt and declining sales. Under Chapter 11 protection, it is closing unprofitable stores and will try to sell roughly 400 of its better performing stores as it looks to stay alive.
Lampert's hedge fund, ESL Investments, is already in talks about potentially acquiring Sears, according to recently filed bankruptcy court documents. It is also in talks to contribute money to support the company through its bankruptcy, through what is known as a debtor-in-possession loan.
ESL Investments owns about 19 percent of Sears shares outstanding, according to the last data compiled by Factset. Lampert owns roughly 31 percent.
Lampert, who stepped down as CEO on Monday after five years in the role, said the speech marked the "second most difficult public speaking event" in his lifetime. The first was speaking at his father's funeral 41 years ago.
In the speech, Lampert admitted missteps and spoke of unexpected challenges.
"When Sears and Kmart merged in 2005, I envisioned a company that would be different and relevant for the 21st century. ... These were two, iconic companies that had lost their way," Lampert said, adding he had seen an opportunity in transforming the two together as a different kind of retailer.
"As we all know, we haven't capitalized on this opportunity the way I would have liked," he added. "Instead of growth and investment we have faced retrenchment and restructuring."
Sears hasn't turned a profit since 2010, limiting its ability to invest in the company and for the future. It has faced bigger competition from better-capitalized competitors like Walmart and Target and has battled the rise of online shopping. Its 140,000-square-foot stores have begun to seem monstrous as foot traffic has dropped.
"There were mistakes along the way, for which I take responsibility. Those failures have affected me in many ways far greater than any successes I have had," said Lampert, who remains chairman of Sears Holdings.
Lampert has been accused by some of stripping the company's business to pay its debt, when its ability to generate sufficient cash flow through operations faltered. Since its merger with Kmart, Sears has spun off its Lands' End clothing brand, sold the Craftsman tool brand to Stanley Black & Decker and closed hundreds of stores. It spun out 250 of its best properties into real estate investment trust offshoot known as Seritage.
It has a pension of roughly 100,000 retirees that, as of January, was underfunded by $1.5 billion, according FactSet.
"But I do want to be clear about one thing. There was never ever a question for me that we must do what we can to protect and honor our associates and retirees. That is because of who I am as a person and who we all are as a company," Lampert said.
The 125-year-old company has more than 68,000 employees, according to bankruptcy documents filed Monday. The court approved its motion to continue its operations during bankruptcy, as well as continue to pay its employee wages and benefits. It will continue to honor member programs, including warranties and promotions.