The chief investment officer of one of the country's biggest public pension funds said the government response to the coronavirus should be focused on supporting unemployed workers, not stocks owned by pensioners.

"I don't buy in to just [saving] the pensioners. Yes, they're important, but they're a small percentage. I think we have to start saving individual people," Christopher Ailman of CalSTRS said on "Squawk Box."

The $2.2 trillion CARES Act passed by Congress and other actions by the Federal Reserve have created an unprecedented economic support from the U.S. government as the coronavirus pandemic shut down large parts of the economy.

On Tuesday, the major airlines and the Treasury Department struck a deal on how the companies could receive payroll support to stay afloat and keep workers employed.

Ailman said it is "such a tough call" as to which companies should be helped, but he said the total amount would likely have negative economic effects long-term.

"It's a question of overall cost. All of a sudden, 'too big to fail,' remember that term from '08? Now we're implying that almost everything is too big to fail, and I hate to say it, but in capitalism we should have some destruction, even from events that people can't foresee. It's just different with this being a health crisis," Ailman said.

Government support of airlines has come under criticism, with some, including Social Capital CEO Chamath Palihapitiya, saying it would be better to let them fail.

CalSTRS, which stands for California State Teachers' Retirement System, has more than $225 billion in assets under management, making it the second largest public pension fund in the U.S. The CalSTRS investment team is still positioned defensively, Ailman said, and expects a slow economic recovery.

"We stopped the economy almost on a dime, which is amazing, but I don't think we're going to be able to restart it as efficiently. We're going to end up stumbling out of this slowly," Ailman said.