Mayor Bloomberg yesterday said he was puzzled by the backlash against his administration’s new policy to turn away homeless individuals from city shelters if they have somewhere else to stay.

“I will say I don’t understand what the brouhaha is,” Bloomberg said on his weekly radio program.

“I don’t know that anybody really wants to look the public in the eye and say, ‘We’re going to pay for services, even if they’re not needed.’ And everybody would say, ‘Of course, only if they’re needed.’ Well, only if they’re needed; you’ve got to find out whether they’re needed. That’s all we’re trying to do here.”

Advocates are suing the city to block implementation of the stricter policy, as is City Council Speaker Christine Quinn, a longtime Bloomberg ally.

The mayor pointed out that homeless families are already subject to those rules.

But Quinn called the new homeless policy “cruel,” saying that many of the single applicants for shelters have mental problems and would be hard-pressed to maneuver through a stricter bureaucracy.