Texaco Corp., the nation's third-largest refiner, reported today that its fourth-quarter profits fell 6 percent and attributed the decline to the recent Saudi Arabia crude oil price increase, lower production and higher exploration expenses.

Texaco earned $500.3 million ($-1.86 a share) in the October-to-December period, down from $534 million ($1.97) ayear earlier. Revenues, however, rose to $14.1 billion from $12 billion.

Texaco's operating earnings for 1980 were up 22 percent to $2.2 billion ($8.31) from $1.8 billion ($6.48) in 1979. Revenues climbed to $52.5 billion versus $39.1 billion.

Standard Oil Co. (Indiana), ranked 6th among U.S. oil companies, announced its fourth-quarter earnings rose 9 percent to $402.2 million ($1.38 a share) from $368.7 million ($1.23)9 Revenues rose to $7.7 billion against $6.1 billion.

For the full year, Indiana Standard's profits were up 26 percent to $1.9 billion ($6.54) on revenues of $27.8 billion from $1.5 billion ($-5.12) on revenues of $20.2 billion in 1979.

Ashland Oil Inc., the nation's 17th-largest refiner, reported earnings for the first quarter of fiscal 1981 ended Dec. 31 dropped 73 percent to $20.2 million (55 cents a share) on revenues of $2.07 billion from $75.9 million ($2.44) on revenues of $2.03 billion a year earlier.

Ashland said its plunge in quarterly profits resulted in part from "the depressed level of economic activity in the United States and a reduction in fuel use by motorists and industry."

Ashland's first-quarter included a gain of $16.5 million from the sale of assets, Ashland said.

Today's reorts followed announcementsThursday by Mobile Corp., Standard Oil Co. (Ohio) and Getty Oil Co. of modest quarterly earnings gains.

Texaco said its 1980 earnings figure excludes an extraordinary credit of $402.3 million ($1.48) from the sale of its interest in Belridge Oil in the first quarter of the year. Including the credit, income came to $2.6 billion ($9.79).

Texaco Chairman and Chief Executive John K. McKinley said the fourth-quarter earnings drop reflected a continued U.S. decline in gross liguids production and increased expenses for expanded exploration activities.

He said reduced profit margins adversely affected U.S. refining operations. Moreover, higher petroleum-product prices failed to cover higher foreign crude oil costs, including Saudi Arabia's $2-a-barrel crude price increase, retroactive to Nov. 1.

Texaco's fourth-quarter results also reflected foreign currency translation losses of $26.9 million. Currency losses for the year totaled $69.6 million.

Ashland Chairman Orrin E. Atkins said U.S. refiners have been operating at about 75 percent capacity because of slumping demand and reduced fuel use by both consumers and industry.

He said Ashland Petroleum Co., Ashland's subsidiary, had sharply lower earnings in the latest quarter due to these conditions. The subsidiary underwent unscheduled shutdowns at three of its plants.