The Hall of Famer said he gained respect for Bryant when he had to talk to him about not passing to his teammates.
Kobe and Shaq spent eight years together with the Los Angeles Lakers, combining for three NBA titles.
The two fell out of favor by 2004, leading O'Neal to be traded to the Miami Heat.
The relationship was repaired years later, and Shaq has been publicly emotional following Bryant's January death.
"I haven't felt a pain that sharp in a while," he said on TNT last month, via Steve Almasy of CNN. "I lost a little brother."
"Kobe was so much more than an athlete, he was a family man," O'Neal said on Twitter following the crash. "That was what we had most in common. I would hug his children like they were my own and he would embrace my kids like they were his."
During Monday's celebration, he was able to discuss a funny story that brought a laugh to everyone in the crowd.