Morgan, who has been a judge on the NBC talent show since it began, announced this week that he had departed the series in order to concentrate on his commitments to CNN's Piers Morgan Tonight.
Speaking on CBS's The Talk after the news broke, fellow judge Osbourne said: "I am so sad. He is a really good guy. He comes off as this pompous know-it-all British stiff ass but he's a really good friend."
However, Osbourne went on to say that she understood Morgan's decision to spend more time working on his CNN show and with wife Celia.
"His wife is pregnant - she's about to give birth any day - and he has CNN and two shows that he hosts in the UK, and the election is coming up. He's like, 'I just can't do it all and I need to be with my wife and concentrate on CNN - something has to go'."
Osbourne added: "I get it but I'm upset for me! It just doesn't seem right to be there without Piers, somehow. I'm really sad by it."
She also referenced his exit on Twitter, writing: "I woke up this morning, thought I had a dream that Piers resigned. Now I'm waking up to the reality. Dont go. Never thought I would say this."
Howie Mandel, the third judge on America's Got Talent, reacted to the news on his Twitter account earlier this week, joking: "I guess I'm more annoying than I thought. I'll miss you @piersmorgan (sic)"
Auditions for the seventh season of America's Got Talent are currently underway at cities across the US.
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Watch Sharon Osbourne talking about Piers Morgan on The Talk below: