Revenue ticked up 1.6 percent to $4.17 billion but fell short of the $4.20 billion that analysts expected.
Expenses rose faster, however, by 3.1 percent. Labor costs rose and maintenance costs jumped significantly as the airline continued to overhaul the cabins inside many of its planes.
Spending on fuel, the airline's biggest expense, rose a modest 0.7 percent. Southwest is forecasting a welcome drop in its first-quarter fuel bill, to $3.30 per gallon from $3.44.
The cost increases were still less than some analysts expected. Standard & Poor's analyst Jim Corridore said he expects revenue to rise faster than most costs in 2013.
The average fourth-quarter fare on Southwest and its AirTran Airways subsidiary was $148.02, up 5.4 percent from $140.38 a year earlier.
Passengers flew 1.4 percent fewer miles on Southwest than a year earlier, and planes were less full — 79.6 percent occupancy, down from 80.5 percent.
Southwest earned $421 million in 2012, its 40th straight profitable year, a streak that Kelly called "a remarkable feat and a record unmatched in the airline industry."
Southwest shares rose 3 cents to $11.39 in afternoon trading. They have gained about 50 percent since last August, rising along with other airline stocks. Investors have been encouraged by stronger financial performance at the airlines and the possibility that a potential merger of American Airlines and US Airways would increase the industry's ability to raise fares.