Top executives at General Electric (GE) and Bank of America (BAC) have made startling statements: We goofed.

This is unusual in a time when many top executives are blaming unnamed gremlins and forces beyond anyone’s control for their mistakes. 

Jeffrey Immelt, General Electric’s CEO, turned down an $11.7 million bonus 2 weeks ago. In a letter to shareholders, he took responsibility for GE’s low stock price and said he would work to rebuild investors’ confidence in the company.

“Our company reputation was tarnished because we weren’t the ‘safe and reliable’ growth company that is our aspiration,” Immelt said in a letter to shareholders. “I accept responsibility for this. But I think the environment presents an opportunity of a lifetime.”

GE’s stock fell about 56% in 2008 and closed Monday at its lowest level since May 1993. The company’s finance business, GE Capital, has been pounded in the recession, and is a real concern. Immelt says he expects GE Capital to generate about 30% of the company’s profit this year, down from about 50% in 2007.

“We intend to reset this business to be smaller, less volatile and more connected to the GE core,” Immelt wrote.

GE cut its dividend to $0.10 a share from $0.31, a decision that will save about $9 billion a year. It was the first time the annual payout has been reduced since 1938. Immelt bought 50,000 shares in the company to underscore his confidence in its future.

Meanwhile, Bank of America’s CEO Ken Lewis said his request for $20 billion in federal bailout money to cover losses at Merrill Lynch was a “tactical mistake” that made the bank look as wobbly as Citigroup (C).

Lewis told the Financial Times that he plans to remain on the job until it pays back $45 billion it received from the US Treasury as part of the bank bailout. This is the first suggestion that he plans to leave the company.

Lewis told the Financial Times that an “abundance of caution” led him to accept more federal aid than needed to absorb Merrill Lynch’s $15 billion fourth-quarter loss.

“In hindsight, it was a tactical mistake, because it put us in the same category as Citigroup,” he told the Financial Times. “We could still have had 8% Tier-1 capital after a $15 billion loss, but we wanted a cushion.”

Lewis said he should have requested $10 billion, because the lower amount might have eased investor fears that there was more trouble ahead for the bank.

As the shrinks say, the issue must be defined before you can overcome it.

Great. Now what?