Austin Box was expected to be the Sooners' starting middle linebacker this fall as a senior.
"Every parent's worst nightmare is to get that call," he said. "We're numb, heartbroken."
Venables said the team had all been notified of Box's death.
"News travels fast, but you want to inform people the right way, the appropriate way," he said. "Guys got together rather quickly and did it the right way."
Box was found unresponsive at a home outside Oklahoma City on Thursday morning. Paramedics arrived, and he was eventually airlifted to a hospital in Oklahoma City, where he died.
An official at the Medical Examiner's office in Oklahoma City told ESPN.com that the cause of death would likely remain unknown until Friday at the earliest.
The 911 call was released on Thursday afternoon, in which Box's friend, J.T. Cobble, attempted to perform CPR.
"There's a guy who stayed with me last night and he's not responding to me," Cobble said when asked what was happening. "He takes pain pills and he's not responding to me."
Asked whether Box was breathing, he said, "I don't think so."
Venables said he "wouldn't be surprised" to see Oklahoma dedicate its season next fall to their former teammate.
"You talk about adversity, but he faced a lot," he said. "He fought his way out of it and got himself back in a place to contribute. That meant a lot to him, to not let his teammates down."
Box injured his elbow before coming to Oklahoma, injured his knee in 2008 and missed five games in 2010 after back surgery before the season began.
"He had a profound impact on the success we had," said Venables.
Oklahoma won its final five games in 2010 to win the Big 12 and the Fiesta Bowl.
"He stands for everything that's right about this program. He’s made a ton of big plays, and was instrumental in what we did to finish the way we did," he said. "Without him, I’m not sure we would have finished the same way."
Box finished spring practice atop the depth chart at middle linebacker.
"He was one of the most selfless guys I’ve ever been around, a great leader for us," Venables said. "His greatest fear was to let down great coaches and great players … He wanted to live up to that in some way."