Money from the supporting people programme is for the homeless, refugees, asylum seekers, young people leaving care, the elderly and women fleeing domestic violence.
The YMCA, with which Liverpool city council has a contract, recognises the building is unsuitable and is moving out. Managers aim to find new city premises within the next two years. YMCA deputy chief executive Paul Malone said: "This place has been described as the Hilton of the hostels because a lot of accommodation is worse.
"But that label gives me no pride just because it's the best of a bad bunch. The council has to help sort out this situation."
Liverpool council leader Mike Storey admitted the council's failure.
"We will make sure it does not happen again - we accept the audit commission's findings and are acting upon it.
"Six years ago we were failing in many areas but have made great strides in education and in social service. Changing the culture of the council is a slow process and cannot happen in one great sweep."