Extern said it had been told the Intensive Family Support Service (IFSS) must close.
Charlie Mack of Extern said the staff had worked "tirelessly" to help vulnerable children.
The Department of Health said families would continue to be supported.
"Sadly we are the victims of not having a government in Northern Ireland at the moment," Mr Mack told BBC Radio Ulster's Evening Extra.
"All of the leaders of all the political parties (in Northern Ireland) have said it would be morally wrong if this service was stopped.
"As late as this afternoon we were pleading with the permanent secretaries to reconsider."
In a statement, the Department of Health said the pilot had "now come to an end and work has already started to consider how we successfully apply the learning identified".
"Families will continue to be supported by statutory services," the statement added.
"No cuts have been applied to any services.
"The Belfast Intensive Family Support Service was established in 2014 on a pilot basis for three years. Thus, since its initiation, it has always been scheduled to end on 31 March 2017."
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Forty-seven staff employed by a Northern Ireland charity which works with disadvantaged families have lost their jobs after a three-year pilot scheme ended.