The nation's output of goods and services, squeezed by persistently high interest rates, fell at a 1.9 percent seasonally adjusted annual rate in the second quarter, the Commerce Department reported yesterday.

The inflation rate also dropped sharply from a 9.8 percent annual rate in the first quarter to only 6 percent in the second, the department said. Food and energy prices rose much less rapidly than in the first quarter. With economic activity essentially flat since January and the high level of interest rates helping to push down many sensitive commodity prices, the rate of inflation as measured by the GNP deflator was at its lowest level in three years.

Most forecasters, including those in the Reagan administration, expect no pickup in the economy until late this year or early in 1982, and some believe the second quarter was the opening phase of what would be the nation's second recession in two years.

In updating its forecast last week in connection with the midyear budget review, the administration declared, "Little or no real output growth is expected during the remainder of the year."

Also as part of that forecast, the Reagan economists predicted that the unemployment rate, which was 7.3 percent in June, would average 7.7 percent in the fourth quarter.

Real output -- the gross national product after adjustment for price changes -- had risen at a surprisingly swift 8.6 percent annual rate in the first quarter. But most analysts said a number of statistical quirks had boosted that figure.

The second-quarter decline was broadly felt. In real terms, personal consumption expenditures dropped at a saving from 4.6 percent of their disposable income in the first three months of the year to 5.3 percent.

Business investment in plants and equipment fell at a 6.1 percent rate. Spending for new home construction plummeted at a 20.6 percent rate. Exports and government purchases of good and services went down at a 5.3 percent and a 4.7 percent rate, respectively.

Only a largely involuntary accumulation of business inventories kept the overall decline from being much larger. Such inventories, which rose $4.5 billion in the first quarter, climbed by $20.4 billion in the second as sales of goods declined faster than production schedules were trimmed.

In real terms, final sales, which include all of the GNP except the change in business inventories, fell at a 4.8 percent rate, compared with a 6.9 percent rate of increase in the previous quarter. In the second quarter of 1980, when GNP went down at a record 9.9 percent rate, final sales dropped at a 10.4 percent rate.

The high level of interest rates makes carring large inventories a costly proposition, however, since many businesses borrow to finance them. These high costs could lead this quarter to fewer orders for new goods as businesses try to bring inventories back into line with slower sales.

For instance, new car output did not decline in the second quarter, but only because the number of cars on manufacturers' and dealers' lots went up just as fast as sales to customers went down. Production schedules have already been reduced for this quarter to reduce new-car stocks.

Part of the improvement in inflation was a result of a shift between the two quarters in the mix of goods and services actually produced. If the mix had remained unchanged, as is assumed in calculating a separate inflation measure known as the GNP chain price index, the rate for the second quarter would have been 7.3 percent rather than 6 percent.

For the second quarter, GNP reached an annual rate of $2.881 trillion, up from a $2.853 trillion rate in the first quarter.