The two pilots who made the emergency landing in Philadelphia after the engine blew apart said late on Wednesday that their "hearts are heavy."
Captain Tammie Jo Shults and First Officer Darren Ellisor issued a statement through the airline.
They said they appreciate the outpouring of support they've received from the public and their co-workers as they "reflect on one family's profound loss."
Shults and Ellisor said they were focused on working with investigators and would not be speaking to the media.
'Fan blade 'suffered metal fatigue'
Earlier on Wednesday, Sumwalt told a news conference that the incident began when one of the engine's 24 fan blades snapped off from its hub. He said investigators found that the blade had suffered metal fatigue at the point of the break.
Sumwalt said he could not yet say if the incident, the first deadly airline accident in the United States since 2009, pointed to a fleet-wide issue in the Boeing 737-700.
"We want to very carefully understand what was the result of this problem, and as I mentioned a few minutes ago, I'm very concerned about this particular event," Sumwalt said at the news conference at the Philadelphia airport.
"To be able to extrapolate that to the entire fleet, I'm not willing to do that right now."
Southwest crews were inspecting similar engines the airline had in service, focusing on the 400 to 600 oldest of the CFM56 engines, made by a partnership of France's Safran and General Electric, according to a person with knowledge of the situation.
It was the second time that kind of engine had failed on a Southwest jet in the past two years, prompting airlines around the world to step up inspections.
A National Transportation Safety Board inspection crew was also combing over the Boeing 737-700 for signs of what caused the engine to explode.
Sumwalt said the fan blade, after suffering metal fatigue where it attached to the engine hub, suffered a second fracture about halfway along its length.