The coronavirus pandemic has highlighted the inequality in health care for different classes of American workers, former World Bank chief economist Joseph Stiglitz said Tuesday.

"The coronavirus is particularly nasty to people with pre-existing conditions ... and America is distinguished in having more health inequality than any of the other advanced countries. So as bad as our income inequality is, health inequality is even worse, and the pandemic is really exposing how bad it is," Stiglitz said on CNBC's "Closing Bell."

The virus has now infected at least 584,000 people in the United States and killed more than 24,000, according to Johns Hopkins University. Many cities and states have reported that racial minorities and poorer communities, such as Detroit's black population, have been disproportionately hit by the virus.

Stiglitz, who has extensively researched income inequality, said this showed how poorly paid some workers who are now considered essential have been.

"What's so striking is these are often people that are serving us every day ... they are the people we depend on, and yet we don't pay them very well and we don't treat them very well," Stiglitz said.

Stiglitz also criticized part of the U.S. economic response to the virus for letting unemployment rise at a record rate, pointing to some countries in Europe that have promised to pay at least part of the wages of workers for businesses that have been shuttered.

"Other countries — the U.K., Denmark — have managed their way through an economic downturn as deep as the United States' without anything like the unemployment numbers we are seeing right now," Stiglitz said.

The Nobel prize-winning economist said he does not feel much sympathy for companies that bought back stock with tax breaks and he thinks that the government should get "significant" exposure to the upside, such as stock warrants, in exchange for helping them.

"It's hard for me to feel very charitable toward these companies, and yet now they're getting enormous help from the government even though some of them didn't even pay taxes in recent years," Stiglitz said.