"I'll never get another hug in my life like the ones he gave," Prescott said of his big brother, Jace. "He was my best friend."

Jace tragically died at 31 years old in April ... but the family hadn't disclosed the cause of death until Dak and his other brother, Tad, sat down for a recent interview with Graham Bensinger.

The two Prescott brothers were extremely emotional talking about Jace's death ... with Dak saying he believes their mom's 2013 fatal battle with colon cancer took an indescribable toll on Jace.

"Jace at the time was finishing with school and was home, was with her and watched it," said 27-year-old Dak, who was away from home playing at Mississippi State at the time.

"She couldn't necessarily hide it from Jace because he was there every day. He saw the times where she would have to spend probably 10-plus hours throwing up, this and that, and saw the medicine she had to take."

"And, almost, you can't even put into the words the burden," Dak continued. "It's something only Jace knew. And he didn't necessarily share that. And Jace was never really much of a talker so when something like that was a huge burden on him, he didn't know how to share it. He didn't know how to be vulnerable about it."

Dak says he was asleep when Jace died by suicide ... saying his father had to wake him up and deliver "some of the worst news that I'll ever get."

Dak says he cried for about 30 minutes with his dad and his friends ... and added, "I wanted to ask 'Why?' for so many reasons."

The NFL star says he's now imploring others to open up about their struggles ... adding, "It showed me how vulnerable we have to be as humans."

"How open we have to be because our adversity, our struggles, what we go through is always going to be too much for ourselves and maybe too much for even one or two people."

"But never too much for a community or never too much for the people and the family that you love. So we have to share those things."