Furious City Council members lashed out at Mayor Bloomberg’s budget director yesterday, blaming him for cuts to libraries, firehouses and child care.

Budget chief Mark Page also took heat from the council’s GOP leader, James Oddo (SI), for letting pensions, health care and debt-service costs skyrocket during Bloomberg’s tenure.

Councilman David Greenfield (D-Brooklyn) screamed, “Shame on all of you!” to Page for shifting child-care vouchers to a new city agency — a move Greenfield likened to a cut because the services are not equal.

Page blamed rising pension costs — about $8.3 billion next year — as well as increases in debt-service, Medicaid and health-benefit costs largely on Albany, the federal government and previous mayors.