Hundreds of workers who care for some of the state’s frailest residents, including those in nursing homes and dialysis centers, are failing to get their annual flu shot, placing patients with weak immune systems at risk of serious illness or death, health specialists said.

A new state report, which tracked vaccination rates during last year’s flu season, found that many clinics, ambulatory care facilities, dialysis centers, nursing and rest homes, and adult day health centers reported worker vaccination rates well below 90 percent, the state and federal goal for health facilities.

Among the lowest vaccination rates in Massachusetts facilities were nursing homes with 72 percent; clinics 68 percent; rest homes 64 percent; and 61 percent at day health programs, which provide community-based nutritional, rehabilitative, and other services to disabled adults.