Casey told ESPN's Jackie MacMullan the information was leaked to the media before Wood even had a chance to inform his family.
"Christian was upset his name got out there. He didn't release it. And the worst part was it got out before Christian even had a chance to tell his mom," Casey said Friday. "I was very unhappy about that. I told our staff, 'This is unprofessional. This can't happen again.' It was so unfair to our player."
Casey said the entire situation has been a learning experience for Detroit's players.
"These young, healthy guys, professional athletes, they don't think about getting sick," he told MacMullan. "It was a quiet ride on the plane, but nobody seemed really that uptight about whether they had it. It was more that nobody knew when we'd get to play again—or see each other again."
Wood was medically cleared Wednesday after recovering from the coronavirus, per ESPN's Eric Woodyard.
The 2019-20 NBA season is delayed indefinitely because of the pandemic.