The nation's industrial production dropped by 0.8 percent last month, the Federal Reserve Board reported yesterday, shortly after Treasury Secretary Donald T. Regan said on television that the economy was "dead in the water."

The fall in industrial output reversed a one-month improvement in February and confirmed that the economy slid further into recession through March, analysts said. "This is not stagnation, this is continuing recession and decline," Otto Eckstein of Data Resources Inc. commented yesterday.

The March drop in industrial output followed a rise of 1.2 percent in production in February, revised downward in yesterday's release from the 1.6 percent increase originally reported. All the figures are seasonally adjusted.

Economists warned last month that the positive February figure was probably just a fluke due to the weather and the effects of seasonal adjustment.

Production has now fallen for seven out of the past eight months, the Fed release showed. The March drop was not as large as the 2 percent falls recorded in December and January, but it was "widespread and . . . pronounced in durable goods for the home, business equipment, construction supplies and durable goods materials," the Federal Reserve said.

Commerce economist Robert Ortner commented that there is "a very good chance that the Gross National Product in the second quarter may be flat or up," in contrast to the sharp declines in the past two quarters. However, National Association of Manufacturers economist Jerry J. Jasinowski commented that yesterday's Federal Reserve figures indicate "the recession will continue through most of the second quarter."

Total industrial production was down by 3.3 percent in the January to March quarter from the last three months of 1981, the Fed report said. The March level was 8.3 percent below the industrial output peak last July when the economy began to dip into recession.

Industry is unlikely to boost output until consumer demand and sales have picked up unmistakably, experts agree. Government figures released earlier this week showed that retail sales were down in March from February.

Yesterday's report showed the defense and space industry and the auto industry as the two exceptions to the pattern of declining production in March.