The cost of living rose 0.8 percent last month - a 10 percent rate of inflation in annual terms - and the purchasing power of an average hour's pay declined fractionally as wages failed to keep pace with prices.

The Labor Department said the buying power of an hour's work was 0.2 percent lower than the month before, and also 0.2 percent less than a year ago.

The White House acknowledged the news was "not encouraging," as press secretary Jody Powell put it, and said it proved the need to comply with President Carter's anti-inflation plan, announced Tuesday night.

Meanwhile, other economic statistics were published suggesting inflationary pressures may be abating slightly.

The Labor Department said that so-called unit labor costs rose at an annual rate of 5.1 percent last quarter, well below the rates earlier this year. These labor costs per unit of production are an important part of the so-called underlying rate of inflation.

The administration announced at the same time that it now expects the federal budget deficit for the fiscal year that began Oct. 1 to the $38.9 billion, $10 billion less than estimated in July.

The shrinkage came mainly because the government simply spent less than anticipated, and because Congress refused to enact some costly Carter proposals. A lower deficit could help dampen inflation.

Carter told his economic advisers this week he wants to put a near-freeze on all nondefense federal spending next fiscal year - meaning these outlays would decline after taking out inflation. He would allow only Pentagon spending to rise appreciably. His aim is to lower the deficit further.

The administration also released an economic growth forecast for next year, showing it intends to run the economy at low speed to forestall inflation. It has said this before. The new growth estimate is 3 to 3.5 percent for all 1979.

The administration's hope is that this rate of expansion will generate enough new jobs to keep unemployment from rising, and still allow the economy to cool off.

The estimated growth rate is now 3.75 percent for 1978.

The Labor Department also said yesterday that first-year wage and benefit increases called for by major labor contracts bargained so far this year are smaller than for 1977. This year's rate has been 8.8 percent, versus 9.6 percent last year.

Last Tuesday the president called on workers to hold their increases in wages and benefits to 7 percent a year and asked businesses to make sure they raised prices 0.5 percent less in the coming year than they did in 1976 and 1977.

Part of the renewed spurt in the cost of living last month was prompted by an acceleration in food cost increases.

Grocery store prices, which fell in July and were steady in August, rose 0.4 percent last month. Over the last year supermarket prices have risen 11.4 percent. For the same period, overall consumer prices have increased 8.3 percent.

But the costs of most other goods and services rose faster than food prices in September.

Overall housing costs increased 0.9 percent, after arising 0.7 percent in August. For the last three months housing costs have been rising at an annual rate of 10.5 percent.

The Labor Department said that the costs of buying a house rose 1.6 percent last month, while the overall costs of maintaining a house rose 1.3 percent. Renters saw their costs rise 0.8 percent.

Clothing costs rose 0.6 percent, as did transportation costs. Apparel and transportation prices had risen 0.5 percent in August.

On the other hand, medical care price increases were smaller in September. After climbing 0.9 percent in August, the cost of medical care rose 0.6 percent last month.

The government said gasoline prices rose 1.4 percent in September, compared with 1 percent in August and 0.8 percent in July. New rules adopted by the Energy Department that go into effect Dec. 1 could have the effect of raising gasoline prices another penny a gallon at the pump.

The new rules permit gas dealers to raise pump prices to reflect higher rental costs as well as gasoline vapor recovery systems they are required to install for environmental reasons.

Fuel oil prices rose 0.9 percent in September, natural gas prices rose 0.8 percent, while electricity costs declined for the third month in a row.

The overall consumer price index stood at 199.3 percent of its 1967 average last month. That means a selection of goods and services that cost $10 in 1967 cost $19.93 last month.

While all percentage changes are adjusted to account for seasonal price variations, the overall index, by tradition, is not seasonally adjusted.