The 39-year-old star's beloved father died on July 22, less than three weeks after his Back to the Beginning farewell show in his native Birmingham.
Jack has recalled how he cried seeing Ozzy back on stage with his Black Sabbath bandmates because he knew how unlikely it was that the Paranoid hitmaker would ever perform again.
Speaking on Good Morning America, Jack cried as he said: "Before he went onstage, I ran back into the dressing room, and I just gave him a big hug. I just kissed him.
"I was like, 'Crush it. You're gonna do so good.'
"And I was crying. I was in the crowd ... There was this area in the crowd, and I was with my brother. And we both were just crying. Not because ... It wasn't because of feeling sorry for him. It wasn't because we were sad for him. ... it was because we knew it was his last time.
"In hindsight, it kind of was a living wake if you think about it. He got to say goodbye to everyone,."
Jack admitted he and his family, particularly his mother Sharon Osbourne, were not prepared for the "outpour of love" they received following Ozzy's death.
He said: "I know she feels the love [from the public], and that has been such a level that none of us could ever really... You know, I think every child sits there and has this thought about one day their parents won't be there, and what will that be like? It's just a part of being human. We just didn't think of it."
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