Reacting to the Chancellor's Budget Statement on Wednesday, Rt Rev David Urquhart expressed concern that funding for the sector is not sustainable enough.
He said: "I am encouraged by the Chancellor's announcement of £2 billion over three years, but as the Chancellor himself said this needs to be placed on a more sustainable footing."
Bishop David's comments come after a report published by the Kings Fund in November last year warned that an aging population is putting added pressure on social care services.
It concluded: "The inability of successive governments to reform social care has resulted in a failing system that is increasingly unable to meet the needs of those who depend on it."
Among other key announcements made by Philip Hammond in his first Budget Statement as Chancellor included a rise in Class 4 National Insurance contributions for self-employed people.
Bishop David welcomed investment in infrastructure and proposals for T-level qualifications to equip pupils with technical skills.
He went on to say: "Investment in infrastructure and creating a climate where businesses can thrive is welcome and will help to insure us against shocks to the economy that EU withdrawal might yet bring.
"Supporting small independent businesses is vital to our economy and I will look closely at the steps the Chancellor has announced to alleviate the impact of the business rates rise.
"I welcome the announcement of extra funding for technical education and the proposed T-level which should give a fresh emphasis to equipping young people with the technical skills our society needs."
The Chancellor also pledged £100 million for triage projects at A&E departments at English hospitals and a new market-leading bond will be launched to help savers.
Leader of the Labour Party Jeremy Corbyn said the Chancellor's Budget showed "utter complacency" over the health of the economy and Philip Hammond failed to understand the "crisis" facing public services.