The economy faltered last month under the combined impact of the coal strike, bad weather and declining demand for automobiles.

The Federal Reserve Board reported yesterday the largest one-month drop in the output of the nations's factories, mines and utilities since the 1974-75 recession. And January retail sales fell 3.1 percent - the biggest decline since the Commerce Department began compiling sales information this way in 1967.

Most of the fall in industrial production was caused by reduction in automobile output, not by the coal strike. In fact, administration economic officials said yesterday they do not think the 72-day-old strike will cause severe disruptions in the econmoy at least for another month.

Severe snowstorms across the northern half of the country plagued retailers in January but declining automobile sales also hit hard too.

Commerce Department chief economist Courtenay M. Slater said that 40 percent of the drop in sales was caused by declining consumer demand for automobiles. Some of that was due to the weather, which kept buyers out of showrooms, but much was caused by consumer resistance to higher prices and to the new 1978 models themselves, she said.

Major automobile makers, including General Motors Corp. and Ford Motor Co., have announced that anticipated electricity shortages caused by the coal strike in some states like Ohio will force them to curtail auto production and lay off thousands of workers.

But government economists said many of those layoffs will happen regardless of whether generating companies cut back industrial power supplies because manufacturers and dealers have too many cars on hand and want to reduce inventories.

General Motors chairman Thomas A. Murphy said yesterday in Akron that he thinks 1978 will be the best sales year in history for automobiles. Nevertheless, he said production of automobiles was trimmed by 175,000 units during last month's bad weather and that even with a prompt settlement of the coal strike and "maximum overtime, GM's first quarter production could still be more than 100,000 units lower than scheduled originally."

Automobile makers have been reducing output for the last several months, however, before bad weather and power shortages were a problem.

The Federal Reserve Board said that the 0.7 percent decline in industrial production was the largest since a 0.9 percent fall in the output of mines factories and utilities in March 1975 during the worst days of the worst recession since the Depression of the 1930's.

"Severe storm activity over much of the U.S. - which caused widespread absenteeism, shorter work weeks, and some supply disruption - contributed significantly to the decline in output," the central bank said.

"However, a further reduction in motor vehicle output was responsible for a greater part of the overall decline," the Fed said. Automobile makers were assembling cars at an annual rate of 7.9 million vehicle in January, down sharply from the 8.9 million rate of Decemeber which was below November. The central bank noted the impact of weather on car assembles but said most of the reduction "reflected efforts to control dealer stocks."

There was a further decline in coal output, too, the Fed said.

William Nordhaus, a member of President Carter's Council of Economic Advisers, said the coal strike has had little impact outside the coal industry yet and told the Association Press, "we don't foresee any major economic impact for the next month."

But while the overall impact of the strike is expected to be small - Nordhaus said it would probably shave only one-quarter of 1 percent off the nation's first quarter growth rate - some areas of the country will be hit hard.

He told told AP that the 6.3 percent unemployment rate could rise a little for a short period, but said so far "there has been no noticeable effect on unemployment."

Another government economist said that much of the job-time and production lost because of the bad weather or electricity shortages will be made up when the weather improves and the coal strike ends.