A Home Office spokesman said the comments were irresponsible.
"We do not expect forces to stop providing essential policing services and it's utterly irresponsible to use language like this," the spokesman said.
"The government has been clear that the police must play their part in tackling the deficit, but that savings can and must be made while protecting the frontline."
Fahy has since told the BBC that his main point was that police officers, health professionals, social services and youth offending teams will have to work together in a more joined-up approach to tackle problems.
"If we can integrate the way we work with other public bodies, and work cleverer with more imagination then we can achieve a lot more with the money available," he said.
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