Corporate profits fell $45 billion during the final three months of 1977 mainly because a jump in inflation boosted the cost if replacing inventories, the Commerce Department reported yesterday.

At the same time, the agency said that it had revised downward its estimate of overall economic growth during the last quarter.

The department said the so-called real gross national product-total output of goods and services adjusted for inflation-rose at an annual rate of 3.8 percent during October, November and December.

The department initially estimated third quarter growth at 42 percent last January and revised that down to 4 percent last month.

he weather and the coal strike are expected to slow economic growth even further during the first three months of 1978, but administration economists expect a rebound-similar to one that occured in early 1977 after severe weather-to make up lost output and wages later in the spring.

Even though the overall economy slowed in late 1977 and early 1978, the unemployment rate continued to fall, in part, officials say, because of the impact of the public service jobs programs Congress enacted last year because employers are hiring more fulltime workers and relying less on overtime.

The unemployment rate was 6.1 per cent in February , its lowest level in more than three years.

For 1977 as a whole, the economy grew 49 percent. Economists say that real gross national product must grow at least 4 percent a year to bring down inflation.

The department also lowered its inflation estimate for the fourth quarter, but it remained much higher than in the third quarter. It said that the overall inflation rate for all goods and services was 59 percent in the third quarter, down from its initial 6.2 per cent projection, but higher than the 48 percent rate of ththird quarter.

Commerce Department Chief economist Courteney M. Slater said that the fall in corporate profits does not indicate much of anything except that inflation in the third quarter was higher than in the fourth quarter.

The agency makes an "inventory valuation adjustment" to take the effects of inflation out of corporate profits. It said that profits from current production were running at a $144.5 billion annual rate in the fourth quarter compared with $149 billion in the third quarter.

Before-tax profits, which do not include the adjustment for inventories, increased $5.2 billion to $178 billion, the Commerce Department said.

The profits from current production also removes depreciation from the overall profits figure. The department said that it subtracted $14 1 bilion for inventory profits and $194 billion for depreciation from the pre-tax book profits of $178 billion.

In the third quarter, the inventory adjustment was only $5.9 billioand the depreciation, or capital consumption, allowance was $17.9 billion.