Among the 1.9 million Scottish households whose minimum needs are covered in the research, one in five fell short of this standard in 2011/12, a rise of 70,000 from 2008/9.
Anti-poverty campaigners in Scotland blamed the rise on benefit cuts and called for a government rethink.
The Joseph Rowntree Foundation report examined income adequacy as measured by the Minimum Income Standard (MIS), a gauge to what he public think we all need for a socially acceptable standard of living.
The researchers from the Centre for Research in Social Policy (CRSP) at Loughborough University found that, of the 390,000 households, 88,000 have less than half of MIS, while 212,000 had less than three-quarters of the amount needed.
Across the UK, the study also found that 4.7m people in couple households with between one and four children (28%) lacked the income required for an adequate standard of living in 2011/12, up from 3.8 million (24%) in 2008/9.
John Dickie, head of Child Poverty Action Group in Scotland said: "The sharp rise in the number of families who don't have the income needed to meet the publicly accepted minimum standard of living is a result of the Coalition government's cuts to the tax credits and benefits families rely on whether they are in or out of work.
"It's clear too many parents just don't have the incomes needed to give their children a fair start in life.
"There can be no excuse now for UK ministers. They must rethink their draconian welfare cuts and ensure the new universal credit actually meets the costs of childcare and genuinely supports families."
Oxfam Scotland called for a Poverty Commissioner for Scotland to "ensure the voices of the poor are heard in the corridors of power" and make sure new polices are designed to reduce poverty and low incomes.
Jamie Livingstone, acting head of Oxfam Scotland, said: "We need a society where every individual and every family has a decent income that allows them to live with dignity.
"This research shows that we are failing to provide that for one in five households in Scotland."
Martin Crewe, director of Barnardo's Scotland added: "We need to see concerted action by all the organisations that work with children and families to work together to address the growing deprivation of vulnerable families, and give a renewed focus to eliminating the scourge of child poverty once and for all."
The study also found that 480,000 people in the UK under 35 living alone (42%) could not afford a decent living standard in 2011/2, up from 310,000 (29%) in 2008/9.
And 800,000 people in pensioner households (9%) lacked the income required for an adequate standard of living in 2011/12, up from 650,000 (7%) in 2008/9.
The Scottish Government said it was doing "all it can" to alleviate the burden of poverty "despite Westminster's programme of welfare cuts".
This included providing an additional £9.2 million to the Scottish Welfare Fund, as well as allocating £74 million in 2013/14 to tackle fuel poverty and supporting the Scottish Living Wage.
A government spokesman said: "If Scotland were to become independent, we would have full control of the welfare system.
"Only then will Scotland have the powers needed to guarantee that our most vulnerable individuals are protected."