UK ministers are considering transferring responsibility for Attendance Allowance, paid to over-65s with a physical or mental disability.
On Thursday, Mr Jones told a House of Lords committee he opposed this, and the devolution of welfare generally.
He said he was "firmly of the view" that the benefits system should remain "at a much wider level".
Mr Jones was giving evidence to the Constitution Committee's inquiry into the UK union and devolution.
"I'm not in favour of devolution of welfare benefits," he said.
"There's talk now of Attendance Allowance being devolved.
"Again, it's not something that we would push for."
Mr Jones said that 7.1% of those claiming Attendance Allowance were from Wales, but only 4.8% of the UK population lived there.
Under the Barnett formula, which decides how much money the Welsh government receives from Westminster, he said Wales would only receive 6.2% of the budget and would therefore "lose out".
"So, I'm firmly of the view that there are some issues - and the benefits system is one of those issues - that should remain at a much wider level," he said.
Welsh Conservative leader Andrew RT Davies agreed that "for the forseeable future" it was better to maintain a "unified welfare state for the whole of the United Kingdom".
Leanne Wood, the Plaid Cymru leader, said the "best way to secure redistribution", from wealthier to poorer  parts of the the UK, was to replace the Barnett formula with a "needs-based formula".
This would end Wales' "historic underfunding", she said.
Welsh Liberal Democrat leader Kirsty Williams told the committee there was a "consensus" amongst the Welsh political parties that the Barnett formula needed to be reformed, but the difficulty was "being able to convince the Westminster government".
Wales would "lose out" if more welfare benefits were devolved, First Minister Carwyn Jones has warned.