A national disability rights and advocacy organisation has said the smaller than expected budget deficit has come at the expense of people requiring social security support.

On Tuesday the treasurer, Josh Frydenberg, revealed expenditure in this category came in at $6.3bn less than estimated in the 2017-18 budget, with national disability insurance scheme (NDIS) payments down $2.5bn.

Therese Sands, joint chief executive of People with Disability Australia, said it was worrying to see such a significant amount unspent on the NDIS had contributed to social security and welfare savings.

“This means people with disability aren’t getting access to the essential disability services that they need,” she told Guardian Australia.

“People with disability are telling us every day about problems they are having in getting enough supports from the NDIS to make sure they can live an equal and good life.”

The underspend emphasised the need to remove the arbitrary National Disability Insurance Agency’s [NDIA] staffing cap, which disability advocates have said forces the scheme to rely on contractors and outsourcing, exacerbating delays in access. Labor has pledged to remove this cap.

“We need the government, and the NDIA, to refocus the NDIS to make sure that people with disability aren’t missing out,” said Sands, whose board and staff are all people living with a disability.

“This budget news also showed how essential it is to lift the rate of Newstart. Many people with disability have been shifted from disability support pension onto Newstart and it is urgent that changes are made to the disability support pension so that people with disability can get the basic income support they need. Our nation’s prosperity needs to be shared with those with the least.”

When the prime minister, Scott Morrison, was pressed by the ABC’s Fran Kelly on the issue of raising Newstart on Radio National on Wednesday morning, he said it would be “a very expensive undertaking and there is not the room in the budget at this point to do that”.

He added that despite the savings the budget remained in a $10bn deficit.

“So while that is the best result we’ve had in a decade, it’s still a deficit and the 2019/20 result is still, you know, it’s still a very modest surplus,” he said. “What we will continue to do is consolidate the budget, get it in a strong position so we’re in a position to support the commitments we have made in additional schools funding, in additional hospitals funding, in affordable medicines funding, these are all big priorities, [including] the NDIS.”

A partner with Deloitte Access Economics, Chris Richardson, said the decline in welfare spend should not be seen as part of any “conspiracy” targeting those reliant on social services. He said the unmet NDIS spend was largely because rollout of the program had been slow.

“This is the largest social program Australia has seen in years,” he said. “It’s slower to rollout than people hoped, and the saving is just because it’s been slow. There has also been delayed negotiations with the states. That’s not a permanent saving. The NDIS will eventually cost at least as much as its budgeted to cost.”

He said the figures on social security spending also reflected a stronger economy, which had seen more people enter employment, including those in the age 60-64 years category.

“The flip-side of the economy getting better is it means social security payments are less, for example unemployment benefits.”