"Now, Ty says, 'This award is not mine alone.' The battle that day, he will say, was 'one team in one fight,' and everyone 'did what we could do to keep each other alive.'" Obama said Monday during the ceremony awarding the Medal of Honor to the fifth living recipient from the wars in Iraq or Afghanistan.
Carter, 33, received the award for his action as a cavalry scout with Bravo Troop, 3rd Squadron, 61st Cavalry Regiment, 4th Brigade Combat Team, 4th Infantry Division, during combat operations in the Kamdesh District of Nuristan province on Oct. 3, 2009.
"It's the story of what our troops do for each other," Obama said.
During a brutal assault by the Taliban, Carter repeatedly raced across the field of battle, rendering aid and bringing munitions to his comrades as they battled Taliban militants in the firefight.
Eight American soldiers were killed and 27 were wounded in the attack at Combat Outpost Keating. Taliban fighters attacked the outpost from the mountainsides above the outpost that later was described in an investigation as indefensible.
Carter was the second survivor of the outpost ambush to receive the Medal of Honor. U.S. Army Staff Sgt. Clinton Romesha was recognized in February for leading an Alamo-type charge against Taliban insurgents trying to capture the outpost housing 53 U.S. troops near the Pakistan border.
"This is a historic day -- the first time in nearly half a century, since the Vietnam War -- that we've been able to present the Medal of Honor to two survivors of the same battle," Obama said.
Obama said Carter stepped into raining gunfire and exploding grenades "perhaps 10 times" to help defend the post. He holed up in a Humvee with two others, rolling down the vehicle's windows to fire upon the approaching enemy before escaping to an aid tent.
"He displayed the essence of true heroism," Obama said.
Obama also praised Carter for speaking out about his struggle with post-traumatic stress and urged other soldiers to look Carter for guidance.
"Let me say as clearly as I can ... he is as tough as they come, and if he can find the courage to seek help, so can you," he said.
In a media availability after the ceremony Carter said, "This has been one of the greatest experiences that my family has had, and I'm humbled and honored that I get to represent the soldiers of Black Knight troop and the families of the fallen. ... I'm nervous about living with the responsibility of telling their story."
He said he also represents "the thousands who suffer the invisible wounds of war."
Obama said Carter told him he was hoping to take his children -- 14-year-old Jayden; 8-year-old Madison and 9-month-old Sehara -- around Washington to show them the sights and the history.
"But, Jayden, Madison, if you want to know what makes our country truly great, if you want to know what a true American hero looks like, then you don't have too look far," Obama said. "You just have to look at your dad. Because today, he's the sight we've come to see. Your dad inspires us, just like all those big monuments and memorials do."