Gov. Cuomo yesterday put the first official price tag on the economic damage inflicted on the state by Hurricane Sandy — a staggering $42 billion, with $19 billion in the city alone.

He argued that the devastation wreaked by the storm statewide was worse than what Hurricane Katrina did to Louisiana in 2005.

“Hurricane Katrina, in many ways, was not as impactful as Hurricane Sandy, believe it or not,” Cuomo said. “Because of the density of New York, the number of people affected, the number of properties affected was much larger in Hurricane Sandy than Hurricane Katrina. This puts the entire conversation, I believe, into focus . . . Now Katrina had a human toll that thankfully we have not paid in this region.”

Katrina and its subsequent floods claimed 1,866 lives, compared with the more than 100 taken by Sandy.

Figures released by Cuomo’s office showed 305,000 homes were damaged or destroyed by Sandy, compared with 214,700 for Katrina in Louisiana. The number of businesses hit here was put at 265,300, against 18,700 in Louisiana. There were 2.19 million power outages here, 800,000 during Katrina.

Cuomo put a $41.9 billion price tag on Sandy’s hit to the state, which included both the city’s costs and $9.1 billion in what was described as “mitigation and prevention” of future storms.

Repairs to the subways and commuter rail lines alone were expected to cost about $5 billion.

Katrina’s hit on Louisiana was $80 billion.

Both Cuomo and Mayor Bloomberg are counting on the federal government to cover the tab, a heavy lift at a time of budget battles in Washington.

“Forty-billion dollars to try to finance through taxes would incapacitate the state,” warned Cuomo, who met yesterday with the city’s congressional delegation to discuss the figures.

And New York isn’t alone in seeking federal help. New Jersey Gov. Chris Christie recently estimated the damage caused by Sandy in the Garden State at $29.4 billion.

Bloomberg is headed to Washington tomorrow to try to convince congressional leaders the city needs about $15 billion to be made whole, including $9.8 billion more than what’s usually provided by FEMA.

Officials said the NYPD anticipated spending $100 million on overtime; the Transportation Department planned $800 million in street repairs and $54 million to fix bridges; and the Parks Department was looking at $150 million to repair Rockaway Beach and another $30 million to restore Coney Island’s beach.

Unexpected spending by all city agencies was estimated at $4.5 billion. Uninsured private losses were put at $4.8 billion, and $5.7 billion was claimed in lost business.

“The city will struggle to recover in the long term unless expedited federal funding is supplied,” the mayor said in a press release, noting that Congress had allocated $120 billion after Katrina struck.

He claimed he was optimistic — but chose an odd way to describe that optimism.

“I always think we’re going to win,” said the mayor. “I still think we’re going to get that stadium on the West Side. I still think we’re going to get the 2012 Olympics. I’m always an optimist and never give in.”

The mayor also told landlords of apartment buildings still without heat or electricity that the city is prepared to step in and make repairs they’ll have to pay for if they don’t sign up for no-cost fixes financed by FEMA.

He estimated that about 20,000 to 25,000 residents are still are without power.

Meanwhile, two executives with Long Island Power Authority — which has been heavily criticized for its storm response — resigned yesterday. X. Cristofer Damianos, a member of the Board of Trustees, and Bruce Germano, vice president of customer service, both claimed their decisions had nothing to do with the outrage directed at LIPA.