People should start saving for their future social care costs in the same way that they save for their pensions, Jeremy Hunt has said.
Those in their 20s or 30s should to start to think about care they may need in later life, the Health Secretary added.
Speaking at the House of Lords Committee on NHS Sustainability, Mr Hunt admitted that there is a "serious issue when it comes to social care".
He also said that a greater share of national resources would need to be put into health and social care - with increases coming from taxation.
Mr Hunt told peers: "We are constrained by our economic context. There is a longer term issue and the issue is a complex one.
"In a nutshell we need as a country to start saving for our social care costs as we save for our pension.
"It needs to be a normal and automatic a thing for everyone to do and we need to make sure there is a proper safety net there for those who haven't been able to do that.
"That is a difficult issue because on the one hand you want to encourage saving but we also want to live in a civilised country where there is a safety net below which no-one falls.
"But I do think we need to do some radical thinking about how we tackle that problem because at the moment we're not in that place."
He continued: "There is a longer term problem where we need to get into the habit of saving more when we are younger in the way that we do for pensions.
"One of the complexities in this area is that it is a Russian roulette as to who actually has to pay care costs - one in four of us will pay more than £100,000 but a lot of us will pay absolutely nothing.
"So in that context it is quite hard to persuade people that they need to put aside money when they are younger."
He went on to say: "The name of the game is to find a way of getting people in their 20s and 30s to think that this is actually part of being a citizen to think about what's going to happen when you're much older in a more realistic way than is currently happening."
When asked about the proportion of gross domestic product (GDP) spent on health and care, Mr Hunt went on to say: "We are going to have to find a way of devoting a greater share of our national resources into health and social care without doubt."
Lord Bishop of Carlisle asked him: "And you'd see that funding coming primarily from taxation?"
Mr Hunt replied: "Yes I would."
Earlier, Downing Street indicated that "under threat" social care systems in certain areas of England are set to receive a funding boost from the Government.
On Thursday, Communities Secretary Sajid Javid will announce measures to help areas where social care provision is facing "severe pressures".
It comes after town hall chiefs said they had discussed proposals with ministers to increase council tax bills in England to fill a black hole in funding for adult social care which could otherwise reach £2.6 billion by 2020.
Meanwhile, the head of the NHS in England said social care should be "front of the queue" for an injection of cash from the Government
Simon Stevens, chief executive of NHS England, told the Lords Committee that the knock-on effect of a deteriorating social care offer is now "unarguable".
He also agreed that a lack of social care provision is the "priority crisis" facing the NHS.
Mr Stevens said: "If there were to be any extra money any time soon, then in my opinion, social care should be front of the queue because it is quite obvious that the knock-on consequences of a deteriorating social care offer - not only for vulnerable people, but also into hospitals - is now unarguable.
"I think there is a very strong case for some immediate support now."
Lord Lipsey asked him: "Surely the most immediate, now crisis-level, problem is that there just isn't enough social care.
"You've got 26% less people living at home supported by local authority carers. You've got 5,000 care home beds already lost in the last year and many more under threat.
"So more and more, you've got to put up people in your hospitals because there is nowhere else to go. Isn't that the priority crisis that faces us over the next few years?"
Mr Stevens replied: "Yes it is."