His words did not ease shareholders' concerns about GE's future and its shares fell 9 percent to a fresh 16-year low.
GE is already identifying parts of its hefty finance arm that it will exit in the coming years, Immelt said in his annual letter to shareholders.
"Our company's reputation was tarnished because we weren't the 'safe and reliable' growth company that is our aspiration. I accept responsibility for this," Immelt, 53, wrote.
"No one is more disappointed than I am with the performance of our stock in this tough environment."
But he argued that the 130-year-old company, which he said has weathered nine recessions as well as the Great Depression, would use the current economic downturn to reinvent itself, with a sharper focus on its infrastructure businesses.
"This environment presents the opportunity of a lifetime," Immelt said. "We can participate in the changes required in the broader economy."
GE shares have been pounded down roughly 77 percent over the past year, a steeper drop than either the 44 percent fall of the Dow Jones Industrial average or the 47 percent slide of the broad Standard & Poor's 500 index.
The world's largest maker of jet engines and electricity-producing turbines reported a 22 percent drop in profit last year, with the primary drag its hefty GE Capital finance arm.
"We will be taking a close look at nonstrategic assets in these businesses, such as equipment services businesses, most of our consumer mortgage books and a dozen or so small or subscale commercial and consumer platforms that we will reduce over the next few years," said Immelt, who declined his bonus last year.
The sharp downturn leaves GE with no choice but to scale back its financial-services business gradually, investors said. Last year the company looked to sell its $30 billion private-label credit-card business, but found no takers.
"There's a lot of talk about GE de-conglomerating, spinning off or selling businesses. That's not something you can do in this environment," said Shawn Campbell, principal at Campbell Asset Management in Chicago, which owns GE shares. "You can't squeeze blood from a stone. You don't want to see them make irrational decisions and fire-sale assets just to look like they're doing something."
Immelt asserted that the entire financial services industry would need to be rethought in the wake of a worldwide recession that started with popping of the U.S. housing bubble a bubble that had been created by repackaging mortgages and other shaky debts into ever-more-complex financial instruments.
"This philosophy transformed the financial services industry from one that supported commerce to a complex trading market that operated outside the economy," Immelt said.
Immelt long defended the company's 31-cent-per-share quarterly dividend, holding that up as an equal priority with maintaining GE's triple-A credit rating. GE on February 27 slashed its payout by 68 percent to 10 cents per share, starting in the second half.
Despite that move, Moody's Investors Service has kept its credit ratings on review for possible downgrade. S&P has a negative outlook on GE's debt.
On March 2, Immelt bought 50,000 GE shares in a move to show his confidence in the stock.
GE shares were down 66 cents to $6.94 on the NYSE, on a day broader U.S. markets were up. Earlier they hit a fresh low of $6.90. Their 52-week high is $38.52.