The Home Secretary ordered officers to focus on the harm suffered by residents from yobs in their neighbourhood, rather than just "ticking boxes on a form".
She made the comments in a new Home Office report into eight pilot projects carried out by constabularies across the country to give more priority to repeat and vulnerable victims of anti-social behaviour.
Some of the forces now ring back everyone who phones reporting abuse or vandalism, while others are recording every single incident in a sustained campaign rather than treating them separately, and sharing information with councils and housing agencies.
The change in attitude comes after a series of official reports and high-profile cases have shown how police take anti-social behaviour less seriously than other crimes, letting victims down. In 2007, Fiona Pilkington killed herself and her disabled daughter, Francecca, after they were repeatedly targeted by local youths. She had complained to Leicester police 33 times.
In a foreword to Thursday's report, Mrs May wrote: "It is often easy to overlook the harm that persistent anti-social behaviour can cause. I know that many police forces, councils and housing providers have made great strides over recent years, but we still hear of victims reporting the same problem over and over again and getting an inadequate response.
"These long-running problems - and the sense of helplessness that goes with them - can destroy a victim's quality of life and shatter a community's trust in the police.
"The aim [of the pilot projects] was to focus on the harm that victims experience - rather than just ticking boxes on a form - and to quality identify and deal with the highest-risk cases."
Assistance Chief Constable Simon Edens, the ACPO lead on anti-social behaviour, said that most people and communities can withstand less serious incidents.
But he said some "suffer greatly from apparently minor incidents" either because they are part of a sustained pattern or because the victims are particularly vulnerable.
The report highlighted the case of three elderly women in Sussex, aged 91, 82, and 65, who were plagued by five youths. The gang trampled on roses planted by the late husband of one of the women, and then damaged garden ornaments and threatened to burn her "at the stake". One of the women suffered a heart attack after another confrontation with the youths, but police and other agencies formed a safety plan to support the victims and later made five arrests.
