"I thought I might be killed," she told Alisyn Camerota on CNN's "New Day" on Wednesday.
"Nothing really warranted it ... After I realized none of this really had a reason, I was just thinking, OK, this is the end."
Demonstrators had taken to the city's streets in protest over the death in Minneapolis, Minnesota, of George Floyd -- as well as those of other black men at the hands of police.
Video shows officers in downtown Atlanta breaking windows on a vehicle, yanking a woman out of the car and tasing a man. The vehicle's occupants were later identified as Pilgrim and Young -- students at Spelman and Morehouse colleges, both historically black schools.
The Atlanta protest was one of many held in numerous US cities calling for an end to police violence against black citizens.
"It's probably one of the hardest moments that I've had to face in my life. I just can't even fathom what happened. At this point, I'm just so far gone, it's like I'm trying to remove myself from that situation, but it's really hard to cope with," said Young.
He says he hasn't yet watched video of the incident.
"I have not tried to relive that moment at this point. It's a little too much right now. And I'd rather just, you know, recover honestly."
His wrist is injured and he has about 20 stitches in his forearm along with bruises all over his ribs, Young said.
Pilgrim said the effect of the incident has been traumatizing.
"I haven't even processed the situation and everything that happened," she said. "I don't want this to continue to happen and have more victims who are traumatized that can't sleep, can't eat. I don't want that for anyone else. This is disgusting. This isn't right," she added.
"I just was shell-shocked. I've seen the situation so many times, you know. We have George Floyd, we have so many people dying and it's just senseless.
Breonna Taylor, Ahmaud Arbery, all these people are dying every day, and people are out protesting for this reason. It's still happening at these protests. We see this literally daily. And it's just not OK," said Young.
One of the officers wrote in a police report that he used his stun gun because he was unsure whether Pilgrim or Young were armed.
"As we've seen in the past, (there was an) attempt to assassinate the character of these young people to say there was a gun. There was never a gun," said Young's attorney Mawuli Davis.
Neither Young nor Pilgrim is facing any charges.
"These are two great college students from two fine universities, from great families. So the typical character assassination that they attempt to do just won't work here."
Young called for police reform.
"Change is really all that needs to come from this. There needs to be a total reset in policing," he said.