The loss of thousands of jobs in energy-related industries because of falling world oil prices kept the nation's unemployment rate at 7.2 percent in March, the Labor Department reported yesterday.

The creation of nearly 200,000 jobs in the nation's service sector was basically offset by the loss of jobs in oil and related manufacturing industries.

The most dramatic increase in unemployment occurred in the oil industry, where 42,000 jobs have been lost in the past two months. Additionally, economists said that about one-third of the job losses in manufacturing industries in March were from layoffs in energy-related businesses.

The unemployment rate in March was little changed from the rate in February, which had soared to 7.3 percent from 6.7 percent in January, the biggest one-month increase in nearly six years.

Many economists had expected the rate to drop sharply in March, to perhaps as low as 7 percent, because they believed the increase in February was a statistical fluke.

The fact that the rate changed little last month seemed to justify the accuracy of the sharp rise in unemployment and underscored the problems that the steep decline in oil has wrought, economists said.

The turmoil in the oil industry particularly hurt Texas, where the unemployment rate rose from 6.4 percent in January to 8.1 percent last month.

Jobs in the oil- and gas-extraction industry have plummeted from 618,000 in March 1985 to 556,000 last month. In March alone, 24,000 oil and gas industry jobs were lost.

Although the fall in oil prices in the past few months has improved the inflation picture, it discourages exploration and extraction of domestic energy products because the domestic price isn't high enough to make the recovery of U.S. oil profitable. Consequently, U.S. energy companies shut down operations and lay off workers.

Other oil states reported large jumps in unemployment. State officials in Oklahoma said the unemployment rate for February, the latest figures available, was 7.8 percent, up from 7.3 percent in January. Louisiana officials said the February jobless rate was 13.2 percent, up from 12.7 percent.

The number of factory jobs also declined by 42,000 last month, 130,000 below the level of employment a year ago. In addition to the energy-related layoffs, automobile manufacturers have begun laying off workers because of a large backlog of unsold cars.

Despite the job losses in the manufacturing and oil industries, the overall unemployment rate fell slightly because of a 190,000 increase in new jobs in services and agricultural industries.

White House spokesman Larry Speakes said the unemployment report "reflects a smooth continuation of employment growth since June of 1985, and we expect a continued steady downward trend in the unemployment rate."

The report shows "reasonably strong employment growth and continued success of the Reagan economic agenda in putting Americans back to work in a steadily growing economy." The Reagan administration has predicted the unemployment rate will average 6.8 percent for 1986.

One effect of the weakness in factory employment has been the increase in people working part-time because they cannot find full-time work or because work is slack, the Labor Department said.

The number of these part-time workers jumped by 161,000 in March, from 5.377 million to 5.538 million.

"Many of these people formerly were employed full time in the nation's factories," said Janet L. Norwood, commissioner of the Bureau of Labor Statistics.

"The continued weakness in employment in manufacturing has made it more difficult for these economic part-timers to improve their situations," she said.

"The February jump in unemployment was not an aberration as the administration has claimed," said Henry Schechter, an economist with the AFL-CIO, who blamed imports for manufacturers' problems.

As oil prices and interest rates began their steep declines late last year, many economists said that it should provide a strong boost to the economy.

However, many indicators suggest that economic growth in the first three months of the year has been sluggish despite lower interest rates and reduced inflation resulting from the oil price drop.

Several economists said yesterday that they still expect the economy to pick up later this year, as lower interest rates and prices put more money in the pockets of both consumers and businesses.

But the oil price decline will create more havoc first in the form of job losses and lower retail sales.

The Labor Department also reported yesterday that the number of discouraged workers -- those who say they would like to work but are too discouraged to seek it because they think no jobs are available -- was 1.1 million during the first quarter this year, compared with 1.2 million in the fourth quarter last year.

"Blacks continue to be disproportionately represented among the discouraged," Norwood said. "Blacks make up less than 11 percent of the labor force but account for 30 percent of the discouraged group."

The unemployment rate for men was unchanged at 6.2 percent, and the rate for women dropped from 6.7 to 6.6 percent. The rate for teen-agers fell from 19 percent to 18.2 percent.

The unemployment rate for whites dropped from 6.4 to 6.2 percent, and for blacks it also declined from 14.8 to 14.7 percent, the Labor Department said.

The rate for black teens rose from 39.1 percent to 43.7 percent, and the rate for Hispanics dropped from 12.3 percent to 10.3 percent last month.

The unemployment rate, including members of the armed forces stationed in the United States, fell from 7.2 to 7.1 percent.