Earlier on CNBC, Greenlight Capital's David Einhorn defended his proposal for Apple to offer current shareholders perpetual preferred stock to deliver value. He is also filing suit against Apple over a proposal to eliminate preferred stock.
Sacconaghi said, "The broader issue Mr. Einhorn is bringing to the table, and one esteemed investor Bill Miller raised yesterday, is that investors are dissatisfied with Apple's capital allocation policy, specifically returning cash."
But investors and analysts are divided on exactly how Apple should proceed. "I believe that Apple should look to take on debt at very low rate and dramatically increase its dividend," Sacconaghi said. "Others believe that Apple should return more cash through buybacks."
He added, "The fact is for a company to have $137 billion and to be adding $40 billion a year is destroying economic value for shareholders."
About $85 billion of the Apple cash pile is overseas, so any major cash return would likely mean it will have to pay taxes on that cash — something Apple appears reluctant to do, Sacconaghi said.
But a major change in capital allocation policies could be what finally turns around Apple's share price, Sacconaghi said, telling CNBC a 15 percent dividend hike wouldn't be enough.
"I think really to get value investors, who are the constituent Apple needs to tap into to own the stock to really move it, you need the dividend in the high 3 percent range," the analyst said. "Ideally, you want a 4-percent-plus dividend. That will really get the stock moving."
—By CNBC's Justin Menza