The timing for the hiring freeze that Mayor Bloomberg announced last week could mean problems: Just four weeks ago, several thousand city workers took City Hall up on its offer of early retirement, and now, since agencies can’t fill those jobs, remaining workers expect their programs will suffer.

“We’re already understaffed and overworked,” said Mark Rosenthal, president of Local 983 of the American Federation of State, County and Municipal Employees, which represents parks department employees. Services “won’t be as good as they were before,” he added. “It’s as simple as that.”

On October 8, 4,006 city employees officially started their retirement, thanks to a package offered to workers who’ve been with the city for at least a decade. The incentive: an additional month’s pay for each year they qualify for pension service.

While some agencies were able to replace the retiring workers before City Hall announced the freeze last week, many positions are still unfilled, leaving the remaining workers wondering how they will get all the work done. And some government watchdogs hope the city will use this as an opportunity to streamline some of the city’s agencies.

At the Human Resources Administration, the loss of 1,030 of its 14,000 employees makes only a small dent in the agency, but some areas will be hit harder than others: more than 100 eligibility specialists who screen clients for access to benefits and services have left, along with another 100 job opportunity specialists and their associates who help place clients in jobs. In addition, 100 welfare and social work supervisors, who oversee programs from fair hearings to protective services to homecare for people with AIDS, have retired.

About 85 of the Department of Homeless Services’ 2,100 employees also cashed out. Among the homelessness programs hit the hardest: the unit overseeing about 40 hotels housing homeless families. The Family Hotels Program lost about nine of its roughly three dozen city workers, including its director, Senora Selsuy.

Meanwhile, the Administration for Children’s Services lost 340 of its 8,000 employees: among them, about 40 child protective specialist supervisors who oversee the investigation of alleged abuse cases and sign off on the removal of children from abusive situations.

“I think there’s a real brain drain going on,” said Caroline Summer of the National Resources Defense Council. At the Department of Environmental Protection, she noted, the water quality division is “hurting for qualified people.”

Some city government watchdogs are trying to look at the recent retirements as an opportunity. In the current economy, “Cuts are going to happen,” said Rose Anello of the Citizens Committee for Children. While her agency is concerned about the impact the hiring freeze will have on services, she hopes ACS uses this time to “strategically rethink” its system by streamlining and combining disparate resources.