Most financially pressed state governments have not tried to cushion their residents from the impact of cuts in federal aid, and the few that have are making up less than a quarter of the cuts, a new Princeton University study concludes.

The study, by Richard P. Nathan of Princeton's Woodrow Wilson School of Public Affairs, confirms the findings of earlier reports that the Reagan administration's belt-tightening has squeezed the poor harder than any other group.

"The pain, hardship and unhappiness were felt primarily among low-income individuals and families and the nonprofit organizations that provide services to low-income people," the study said.

What is new about the Princteon report is an analysis of two factors that helped shape each state's response: its political ideology and the extent of its fiscal stress. Some conservative states refused to make up the cutbacks, while some liberal states couldn't afford to do so.

The study sampled conditions in 14 states. At one end of the scale was Massachusetts, which, the study said, made up 10 to 20 percent of the cuts in federal funds because it has a liberal ideology and has been under only moderate financial stress.

At the other end was Ohio, which has a moderate ideology but has been under such extreme fiscal pressure that state leaders could not respond to the cuts, according to the study.

Ohio was one of several states that the study said saved money through the cutbacks, which reduced the matching funds the state had to provide to qualify for certain federal programs.

"We didn't try to make up those federal programs with state dollars because the state has been in a continuing financial crisis," said Ohio budget director Cristina Sale. "We've cut discretionary programs: those things that are nice to have but that people don't need to eat. I can't believe anyone has been in a position to afford to make up the federal reductions."

Even after nearly doubling the income tax surcharge, state officials had to cut Medicaid and other benefit programs. But Sale disputed the study's contention that the federal cutbacks saved Ohio money, saying that the recession and federal rule changes caused the state's welfare caseload to swell from 200,000 to 350,000.

"As the federal government has pulled the rug out of subsidies for the poor, we have continued to make up that difference," Sale said. "The state has chosen not to abandon the poor. We could have left a half million people with no income support, but you can't just walk away."

In Massachusetts, legislators responded to a $5 million cut in federal job training funds by adding $5.8 million in state money to the program. And to compensate for cuts in social service grants and a ballot initiative that limits property taxes, the state plans a $157 million package of aid to local governments.

"We're trying to stop the hemorrhaging," said Lt. Gov. John Kerry. "These aren't reductions in force, these are wholesale eliminations of federal programs. There's agreement we ought to be reducing the fat, but our attitude is that the Reagan administration's priorities are screwed up."

While state officials managed to give a 5 percent increase to welfare recipients, Kerry said, "We've just had to bite the bullet on some other things we'd like to do," especially in income-support programs.

Most state officials did little to make up funding for food stamps and Aid to Families with Dependent Children, the Princeton study said, because they did not want to pay benefits that were higher than in neighboring jurisdictions or raise taxes to redistribute money to the poor.

But many states managed to spare such service programs as day care and home health care.

Oklahoma and New York also made up 10 to 20 percent of the federal cuts, the study found, while Illinois, Mississippi, Missouri, Texas and Washington did the least. Few cities provided compensating aid unless, like Cleveland and Rochester, N.Y., they were aided by their strong county governments.