BLOOD ON CUOMO’S HANDS: New York’s coronavirus nursing home death toll didn’t have to be so high.

It’s long been clear the official numbers didn’t capture the coronavirus’ full toll in New York’s nursing homes — but the updated count was nonetheless appalling.

Yet Gov. Andrew Cuomo still won’t admit his administration was wrong to mandate that facilities filled with those most virus-vulnerable take in COVID-positive patients.

The new Health Department info released late Monday adds 1,700 presumed coronavirus deaths to the grim total, suggesting that COVID-19 complications have killed 4,813 residents of nursing homes and adult-care facilities — and that doesn’t include those who died in hospitals.

Cuomo downplayed the count Tuesday: “I would take all of these numbers now with a grain of salt,” since “what does a ‘presumed death’ mean, right?”

Considering how pessimistic Cuomo has been in other areas, such doubt seems self-serving. We know fatality rates are far higher than normal — and the coronavirus has proven most deadly to the elderly and those with certain preexisting conditions. Indeed, Cuomo admitted Tuesday, “We knew the nursing homes were going to be a target.”

So why on earth did his health commissioner, Howard Zucker, force nursing homes to take in virus-positive patients starting March 25?

Why, indeed?