Victims of the shooting rushed to help others even before tending to themselves, said Cone.
"A young lady who had been shot in the hip and didn't realize it immediately took care of one of her buddies," said Cone. "She put a tourniquet on a soldier's leg and carried him out of the facility."
"Only after she had gotten her buddy taken care of did she realize that she herself had been shot," said Cone.
President Obama warned early Friday against "jumping to conclusions" regarding the motive for the shooting and ordered flags to be flown at half staff until Veteran's Day, saying that the "entire nation is grieving."
The president said he had met with the FBI chief to discuss the massacre.
Sgt. Salvatore "Rico" Sanchez told "Good Morning America" that he treated a captain who was nearby when the shooting started. Covered in blood that wasn't his own, the captain escaped unscathed with only a mild case of shock.
"According to the captain that I was treating, [Hasan] was sitting down and he just stood up out of nowhere and started shooting," Sanchez said.
As the sound of gunfire erupted, Sanchez said he heard people yelling to call 911 and "all kinds of cries for help."
Sanchez saw a virtual battlefield with dozens wounded and 13 dead or dying. Their names began to emerge today and each had a heartbreaking story. Among them was Francheska Velez, a 21-year-old soldier who had returned from Iraq three days ago because she was pregnant.
Velez was in the buildling filling out paperwork regarding her pregnancy when Hasan opened up.
Cone said Sgt. Kimberly Munley exchanged gunfire with Hasan and shot him four times despite being shot herself, putting a stop to the carnage.
"She was quite effective, one of our most impressive young policemen," Cone said. "She walked up and basically engaged him. I think, certainly, this could've been far worse."
Cone said Munley spent Thursday night calling her fellow co-workers from her hospital bed to make sure everyone was OK.
The atmosphere at Fort Hood Thursday seemed to be one of chaos, yet also one of quick action and sharp thinking. Numerous reports have described well-trained soldiers who used anything they could find to treat the wounded -- one witness told ABC News that a man's gunshot wound was treated with supplies from a mother's diaper bag.
"It is absolutely inspiring, the actions that soldiers took," Cone said today.
An Army official confirmed that Hasan would have been deployed to Afghanistan later this month, although officials previously said he was being sent to Iraq. Sources told ABC News that this would have been his first deployment.
Maj. Khalid Shabazz, who was Fort Hood's Muslim chaplain until a few months ago, told "GMA" he was "mortified" when he heard the news about the shooting and the person alleged to be behind it.
Shabazz said he had met with Hasan, one of 48 Muslim soldiers on base, on several occasions, and said that while Hasan and others sometimes complained about teasing from other soldiers, "I didn't find him to be depressed at all. I found him to be very pleasant."
Some of the Muslim soldiers, he said, "would complain about being taunted and harassed."
Shabazz said the taunts ranged from mild joking and misunderstandings to sometimes something more and could be "a real problem."