U.S. low-cost carrier Southwest Airlines, which lost a bid to buy Frontier Airlines Holdings Inc, may look for another acquisition but would continue to carry conditions with any bid, its chief executive Gary Kelly told The Wall Street Journal in an interview.

"Even Tiger Woods doesn't win every tournament," Kelly told the paper.

Kelly told the paper that Southwest would likely limit any potential future acquisition to an airline going through a bankruptcy restructuring, and wants to keep an all-737 fleet.

Southwest lost its bid to buy Denver-based Frontier in a bankruptcy court auction last week.

Disagreements over seniority between Southwest and Frontier pilots played a major role in unraveling the deal. Southwest's bid required that the pilots' unions reach an accord.