Public approval of President Reagan continues to decline, according to a new Washington Post-ABC News poll that shows people tend to blame him for rising unemployment but not credit him with reducing inflation.

Overall, 46 percent of those interviewed said they approve of Reagan's handling of the presidency, and 45 percent said they disapprove. A month earlier, 51 percent said they approved and 44 percent said they disapproved. The new rating is the lowest found for Reagan in a Post-ABC News poll.

A majority of the public 53 percent feel that Reagan's program will help the nation's economy in the long run, but that is virtually the only favorable finding for the president in the new poll. Among some of the unfavorable ones are these:

* By 2 to 1, 60 percent to 29 percent, those interviewed disapproved rather than approved of the way Reagan is treating unemployment. While Reagan has said umemployment is a problem he inherited, one third of those in the survey said his administration deserves "a substantial amount" or "a great deal" of the blame and another 41 percent say the administration deserves some of the blame.

* Although government statistics show inflation receding appreciably, a third of the public felt that prices are still rising steeply. Another 40 percent said they are rising somewhat.

* Fifty-six percent of those interviewed said that, where they live, Reagan's presidency has made things worse for people; only 18 percent said he had made things better.

* Sixty-four percent said the president's economic program is hurting the economy right now, compared to 24 percent who said it is helping.

Despite an effort by Reagan to refute charges that he is a rich man's president, that perception of him continues to grow. Fifty-five percent said he cares more about serving upper income people than the rest of the population, compared to 33 percent who said he cares about serving all people equally.

"All his tax reductions are better for the rich, far better than for the poor," said a 50-year old New York widow, a registered nurse who was among those interviewed.

Supporters of the president often maintain that he is being criticized unfairly. A 47-year-old California woman said, "I don't believe he would be openly discriminant. He's just playing the part of a bad guy, but what he's doing had to be done by someone sooner or later, and it just happened to be him." This woman, a housewife, said she liked Reagan "better than those other guys" such as House Speaker Thomas P. (Tip) O'Neil Jr., and she charged that Congress "is full of thieves and crooks."

As has been the case throughout his presidency, different constituencies differ sharply in their views of Reagan. Only 27 percent of the Democrats interviewed gave Reagan a favorable rating, compared to 48 percent of independents and 75 percent of Republicans.

One poll question asked whether "Ronald and Nancy Reagan set a good model for the country in their personal style of living, or not?" Fifty-two percent approved of the Reagans' lifestyle and 38 percent were critical of it, but underlying those figures were sharp divisions.

Men, for example, approved by a 2 to 1 ratio. Women were evenly divided, but working women, representing one-quarter of the adult population, tended to be critical, with 51 percent saying the Reagans did not set a good model. A majority of those with household incomes of less than $12,000 a year also expressed disapproval. But the quarter of the population with incomes of $30,000 a year or more gave a favorable response by 2 to 1.

On another matter, the poll asked a series of questions aimed at finding whether people are more hardput economically today than they were a year ago. "Please tell me whether you have found yourself making the change mentioned or not in the past year," interviewers asked. Some of the "changes" were these:

*Forty percent said they were going more deeply in debt now than a year ago "to make ends meet."

* Thirty percent said they were not repairing their cars "when a serious problem developed."

* Twenty-four percent said they were not getting medical care that they should get.

* Twenty-one percent said they were "selling belongings to raise some money."

*Nineteen percent said they were "skipping meals to save money," 19 percent said they had moved to less expensive housing, and 19 percent also said they were getting behind in payments for housing.

A total of 1,018 people were interviewed in the nationwide survey, which was conducted from May 24 to May 28.