Joining a fairly exclusive club among major U.S. airlines, Eastern Airlines today reported a first-quarter profit of $4.1 million, compared with $3.5 million in the first three months of 1980.

At the company's annual meeting here today, Frank Borman, chairman and president of the Miami-based airline, called the results "far from satisfactory" but added, "We regard the small profit for the quarter as very gratifying in view of the difficulties the entire trunk industry has faced in the past year."

Borman attributed the first-quarter profit to better cost control and improved yields despite a 9 percent decline in passenger traffic for the January-March period, compared with last year's.

Eastern reported operating revenues of $961.5 million for the first quarter, compared with $853.8 million for the year-ago quarter. Operating expenses totaled $947.6 million in this year's period, compared with $836.6 million in last year's. As a result, Eastern produced an operating profit of $13.9 million in the first quarter of 1981, down from a first-quarter operating profit of $17.3 million last year.

After payment of dividends on preferred stock, Eastern showed a loss of 4 cents per share of common stock, compared with earnings of 8 cents a share in the same quarter of 1980.

Eastern said results for the first quarter of 1981 included a $5.2 million pretax gain from equipment sales, compared with a gain of $672,000 in last year's period. The latest results also included a $5.9 million benefit from an actuarial change in pensionfund investment assumptions and a $2.3 million gain on foreign currency fluctuations compared with $1 million a year earlier.

Borman told shareholders the airline's major challenges are the continuing surge in jet fuel prices -- leveled off right now -- and the increasing competition Eastern is getting on its routes as a result of airline deregulation. Borman cited in particular competition from the new low-fare airlines starting out with significantly lower labor costs than the established carriers.

After the meeting, however, Borman said Eastern's Air-Shuttle was doing "very well" in the face of new competition from low-fare New York Air, although he declined to give any numbers.

Borman went out of his way several times to praise Eastern's employes but also noted that they would be called on to continue to help the company with contributions to a variable earnings program -- in which employes contribute part of their salary, which they get back, plus some, if the company produces a profit -- and with further productivity improvements. The challenges of operating in the new deregulated environment "place a severe strain on all of us," he said. Borman said Eastern's major competition will come from Delta Airlines, its long-time adversary, and from small, special-purpose airlines operating in some of its markets.

Borman also noted that Eastern is actively looking at new routes with which to start a shuttle-type operation.