Sears, Roebuck & Co., the nation's largest retailer, reported yesterday that it had slightly lower earnings in the final quarter of 1981 but a 6.6 percent gain for the year.

Meanwhile, Coca-Cola Co. said it had higher 1981 earnings although revenues declined, and Esmark Inc. said results for its first fiscal quarter showed improvement.

Sears's fourth-quarter profits were $333.1 million ($1.05 a share) on sales of $8 billion, down from $339.7 million ($1.07) a year earlier on sales of $7.6 billion.

For the year, Sears earned $650.1 million ($2.06) on revenues of $27.36 billion compared with $609.8 million ($1.93) in 1980 on revenues of $25.15 billion.

Net realized capital gains were $140 million (44 cents) against $48 million the previous year. The gains were principally on the sale of shopping centers and other investments. The 1980 overall results were reduced 13 cents a share by the cost of an employe early retirement program.

Chairman Edward R. Telling pointed out that Sears's interest expense rose 34 percent to $1.52 billion. He said this particularly hurt the company's credit business, resulting in a rise to $83.3 million from $25.3 million in 1980 in the losses on credit operations.

He said merchandising and retailing results improved but that the Allstate insurance group's income tumbled 9.8 percent to $406.3 million from $450.4 million in 1980.

Coca-Cola Co.'s fourth-quarter profits were $106.2 million (86 cents a share), up 10.8 percent from earnings of $95.9 million (78 cents) a year earlier. But revenue fell to $1.41 billion from $1.44 billion.

For the year, the company said net income was $481.8 million ($3.90), which was 14.1 percent higher than 1980 net income of $422.1 million ($3.42), as revenue increased by 4.8 percent to $5.89 billion from $5.62 billion.

Coca-Cola is the world's largest producer and distributor of syrups and concentrates. Products include Coca-Cola, Mello Yello and Ramblin root beer. The foods division produces and markets the Minute Maid brand of frozen concentrate and chilled juices.

Esmark Inc. said that earnings from operations and the 35 percent equity interest in Swift Independent Corp., which was spun off last year, were $13.53 million ($1.01 a share) in its fiscal first quarter ended Jan. 31 on sales of $725.18 million, compared with earnings of $12.28 million (87 cents) a year ago on sales of $678.91 million. The net income gain was 16 percent. Food segment profits were 43 percent higher.

The Playtex division had higher earnings but sales and profits of the chemical, industrial products and high fidelity music divisions all were adversely affected by the recession, with chemical profits hit hardest.