Kelly pinned the earnings miss on a few overly optimistic analyst estimates, but also said fare competition, driven by low fuel costs, played a part.
"Over the last several weeks we've seen a further softening of the fare environment, so it's very competitive out there," he said.
Lower fuel prices have pushed up competition in the U.S. airline industry, allowing large domestic carriers to slash fares to levels offered by budget airlines.
Cheap oil has also forced Southwest, the largest hedger among U.S. airlines, to pay hefty sums to counterparties in hedge contracts that it acquired for protection in case of a rise in energy prices. As a result, the carrier will not reap the full benefit of cheaper fuel.
Kelly said he expects revenue per available seat mile (RASM) to decline of 3 to 4 percent year over year in the third quarter.
RASM, a key indicator of an airline's performance, measures sales against flight capacity.
Southwest's total expenses rose 2 percent to $4.11 billion in the second quarter. However, unit cost fell 2.6 percent, helped by lower fuel costs.
The results come a day after Southwest temporarily halted all flight departures as it worked to resolve issues impacting multiple technology systems.
Kelly apologized, explaining it was caused by a computer network failure that affected virtually all of Southwest's operations and customer-facing systems.
"We depend on phone companies and power companies, et cetera, but this was all on us," he said.
Southwest also said it expected to buy back an additional $250 million in common shares as part of an accelerated share repurchase program to be launched soon.
— CNBC's Tom DiChristopher contributed to this report.