The nation's industrial production dropped another 0.4 percent in November, only half the drop of the two previous months but still concrete evidence of a continuing recession, the Federal Reserve reported yesterday.

The seasonally adjusted decline was the 12th in the last 14 months, and it put the output of factories, mines and utilities 11.9 percent below its peak of July 1981, when the recession began.

Cutbacks in production of motor vehicles, metals and a variety of business equipment were responsible for much of last month's drop, the Federal Reserve said. Declines were registered in every major product grouping except for defense and space equipment.

But except for the production of nondurable consumer goods -- which rose 0.1 percent in October before dropping 0.3 percent last month -- the declines for each product group were uniformly smaller than in the month before.

Many analysts expect at least a small drop in industrial output again this month, but they also note that production of some types of goods, particularly automobiles, probably will be up.

Auto assemblies fell from an annual rate of 4.7 million units in October to 4.5 million last month. On the same seasonally adjusted basis, automakers have announced plans to assemble cars at a 5-million-unit rate this month. Similarly, production of construction supplies, which declined only 0.1 percent in November, might increase in the wake of recent increases in housing starts, analysts said.

Even if the December production figures show only a small decline when they are released next month, any real advance does not appear close at hand, according to most economic forecasters. "I don't think that we are yet looking at the turn, but it could be close," said Alan Greenspan of Townsend-Greenspan & Co. "We are still picking at straws."

A sustained improvement in purchases, principally by consumers, is needed to generate a higher level of new orders for factory goods before production will be increased significantly.

The flow of such new orders has remained weak, and the latest figures for business inventories suggest that companies in many industries still are trying to reduce the stocks of goods they have on hand. That means those companies will seek to keep new orders running below their current level of sales.

As economist Robert Gough of Data Resources Inc. put it, "You're not going to see much of a turnaround until you see a pickup in spending."

His conversations with department store officials lead him to believe that this Christmas season has been "very mediocre for many stores," Gough added.

Last month, production of consumer goods fell 0.5 percent, reflecting the drop in auto assemblies and as well as declines in nondurable goods such as food and fuel, the Fed reported. Business equipment production also went down 0.5 percent, as continued sharp reductions in the output of manufacturing, power and transit equipment were offset only partly by a rise in oil and gas well drilling. The rise in drilling came after 10 straight large monthly declines.

Production of materials fell 0.6 percent, about the same as in the two previous months. Steel output continued to fall and now is running only slightly more than half its average level for 1981.