Researchers at the University of California at Berkeley have released the findings of a study that are tough on the mayor's new prekindergarten program. But we should resist drawing the wrong conclusions from their important research.

The Berkeley study faulted Mayor Bill de Blasio for expanding pre-K in middle-class neighborhoods, when many low-income children still don't have the opportunity to attend preschool.

NYC created 26,000 state-funded pre-K spots in the fall. De Blasio and his supporters have touted the expansion of the city's program as a major accomplishment. (Gov. Andrew Cuomo has bragged about it, too, although he opposed how de Blasio wanted to fund the program. But I digress.)

The researchers analyzed new pre-K spots by ZIP code and compared them to previously available slots. They point out that pre-K programs are more beneficial to low-income kids than their better-off peers, and ask why the mayor would allocate scant resources to children not in dire need.

Policy liberals like to advocate pre-K for poor kids, saying the programs help students learn better and that long-term they help fight poverty and crime prevention. But it's also school, and everyone needs school.

The researchers are right: poor kids need pre-K. But they're wrong to fault de Blasio for trying to serve middle-class families. Everyone should have access to free pre-K, not just the poor. The state should provide more funding to make the program truly universal.

For many middle-class families, paying for pre-K can be an economic stretch. In my neighborhood, one of the most affordable private preschools costs more than $12,000 a year.

But there is another reason why we should not focus pre-K policy exclusively on low-income New Yorkers. Some services for poor people can be of low quality, and can eventually lose public support. For instance, many housing complexes that serve only NY's poorest are dangerous and in desperate need of repair.

The middle class has the political clout to ensure that quality improves and programs, including the ones that serve the poor, continue.

Public education should serve everyone. And it should begin in preschool.

Liza Featherstone lives and writes in Clinton Hill.