The economy grew briskly in the second quarter of the year, but not as rapidly as the Carter administration had hoped, while inflation jumped to 10.1 percent, the government reported yesterday.

Many economists had anticipated an increase of about 9 percent in output during the quarter, but the Commerce Department's report on the gross national product said the increase was 7.4 percent.

Before adjustment for inflation, the gross national product grew 18.2 percent to an annual rate of $2,077 billion, the first time the economy has crossed the $2 trillion plateau.

Commerce Secretary Juanita Kreps conceded to reporters that the second quarter report on output was not good enough to enable the administration to reach its new, scaled-down projections for the year.

In recent weeks, economic activity has slowed measurably for the year.

Presidential press secretary Jody Powell said growth figures represented a "relatively good performance," but called the acceleration of inflation from 7.1 percent pace to a 10.1 percent rate "not encouraging."

Administration officials are worried that continuing high inflation will put pressure on the Federal Reserve Board to raise interest rates even more, as it voted to do last month. [Details on Page D7.]

Economists had expected a more robust showing in the second quarter as the economy rebounded from a dismal winter, when cold weather and snow triggered a small, 0.1 percent decline in production.

Kreps said the economy is expected to grow at a rate beween 3.5 percent and 4 percent for the rest of the year. In the first half, output of goods and services expanded at an annual rate of 3.6 percent. If the administration is right on its second half projections, output will fall short of the 4.1 percent rise predicted by the president on July 6.

If interest rates rise much more, administraion officials such as inflation counselor Robert S. Strauss say, even the modest growth expected in the last half of the year could be choked off.

The economy must grow in the range of 3.5 percent to 4 percent to keep unemployment from rising, most analysts say, although in the last year the unemployment rate has been falling much faster than the rule of thumb would predict.

Real growth is measured by the gross national product, the amount of goods and services produced by Americans in a year. It is the broadest measure analysts have of the economy.

Kreps told reporters that "real growth fell a bit below our expectations while the rate of price increases was higher than had been expected."

She said that forthe first six months of the year the overall rate of inflation in the economy was 8.6 percent - 7.1 percent in the second.

Food prices rose rapidly, at a 17 percent rate, while other prices increased at about 7 percent rate.

Press secretary Powell said the acceleration in inflation from the first quarter to the second underscores the need for business and labor to cooperate with the president's voluntary program to hold down wage and price increases.

Kreps said that, unless inflation is brought under control soon, pressures will increase on the Federal Reserve Board to raise rates to make money more expensive and slow consumer and business buying.

Much of the pickup in economic growth in the second quarter came from increased car sales and general consumer purchasing after the bad winter.

There was also a sharp rise in commercial and industrial construction, and home building remained at high levels. Kreps said that "the encouraging data on June housing starts and building permits issued earlier this week improve the prospects for this sector in the coming months."

Consumer buying increased at an annual rate of 6.1 percent after falling 1.4 percent in the first months of the year. Private investment spending rose at a 12.4 percent pace, following a rise of 11.3 percent between January and March.

In constant 1972 dollars, the increase was at a 7.4 percent rate, up $24.4 billion, to an annual rate of $1,379 billion. The Commerce Department's estimates are preliminary, and will be revised next month when more data are available.

The Commerce Department also reported that it has revised downward slightly its figures of gross national product for 1976 and 1977.