The nation's civilian unemployment rate remained unchanged last month at 7.4 percent, slightly below the rate prevailing when President Reagan took office and virtually unchanged since May.

The Labor Department, in the last major economic report before the election on Tuesday, said 350,000 more people found jobs last month, raising the number of employed Americans to 105.6 million. That is 5.65 million more than when President Reagan took office.

However, 8.4 million people were unemployed in October, 400,000 more than when the Reagan administration began. In addition, 5.5 million people are working part-time because they cannot find full-time work, and about 1.2 million people are too discouraged about job prospects to look for work.

The unemployment figures were hailed by the Reagan administration but condemned by leading Democrats, who said the statistics masked large numbers of people without work and showed that the economy has stalled.

White House spokesman Larry Speakes, during a campaign swing with the president through Michigan, said, "the economy is still expanding and creating new jobs." Speakes said that even though the unemployment rate didn't improve last month, "the promise of new jobs remains brighter than ever."

Democratic presidential candidate Walter F. Mondale, on a campaign stop in Lorain, Ohio, criticized Reagan's jobs policies. He told some jobless supporters, "They've done it to you, now you do it to them," suggesting they should vote Reagan out of his job.

The Democratic Policy Committee issued a study saying that under the Carter administration, 10 million jobs were created, and that the number of jobs created by the Reagan administration "is far less."

Most of the gain in new jobs last month was in the services sector, where about three-fourths of all Americans are now employed, the Labor Department said. Manufacturing jobs increased by 55,000 in October, but they weren't enough to offset the decline of 125,000 factory jobs in September.

"Job growth in manufacturing has been quite limited since early in the spring," said Janet L. Norwood, commissioner of the Bureau of Labor Statistics. "Indeed, manufacturing has recovered only about 70 percent of the jobs lost during the recession.

"After dropping sharply in the early months of the recovery, unemployment has shown little movement since last May," Norwood said.

The unemployment rate was 7.5 percent in January 1981 and declined to 7.2 percent by April of that year. The rate began climbing steadily in August 1981, and reached a peak of 10.7 percent in November and December of 1982.

When the Carter administration began, the unemployment rate was also 7.5 percent and dropped to 5.6 percent in May 1979 before reaching a high of 7.8 percent in July 1980, according to the Labor Department.

Many economists have said that because the rate of the nation's economic expansion is slowing, it will be more difficult to create enough jobs to keep the unemployment rate from rising. Some economists inside and outside of the government said they expected the unemployment rate to rise last month.

The nation's output would have to grow at about a 3.5 percent annual rate to prevent a rise in unemployment, many economists have said. During the third quarter of this year, the economy grew at a 2.7 percent rate.

Economists are divided about whether and how strongly the economy will pick up through next year. Few prominent economists forecast a recession, but many say the economy will continue growing at a markedly slower pace for the next few months.

"With unemployment stalled at 7.4 percent for the last six months, the AFL-CIO is concerned that the growing signs of a new recession will mean a quick return to double-digit joblessness," the AFL-CIO said.

"I thought we might get a slight increase in unemployment," said Lawrence Chimerine, chief economist for Chase Econometrics. He said he had received reports about layoffs in the energy, manufacturing and financial industries.

"On balance, over the last three months the economy has slowed down sharply," Chimerine said. "If it continues, the unemployment rate may start edging up."

The overall unemployment rate, including the armed forces, remained at 7.3 percent, also the same as in September. The rate for adult men declined from 6.5 percent to 6.3 percent, and that for women rose from 6.7 percent to 6.9 percent.

The unemployment rate for whites was unchanged since July at 6.4 percent, while the rate for blacks rose from 15.1 percent to 15.4 percent. The rate for Hispanics rose from 10.7 percent to 10.9 percent.

A Labor Department index that gauges the proportion of industries with new job growth increased from 40.3 to 65.4, which means that nearly two-thirds of the industries surveyed increased employment.

Payroll employment, another employment measure based on a survey of businesses, grew by 440,000 in October, the Labor Department said.

The averge workweek of production workers on private nonagricultural payrolls dropped from 35.3 hours to 35.1 hours. The manufacturing workweek declined 0.1 hour and factory overtime was unchanged at 3.3 hours, its level for the past six months.