She made the comment when talking about how she felt after learning that her ex-fiancé Luke Worrall had cheated on her with Elle Schneider, who is awaiting gender reassignment surgery.
Osbourne has written an open letter of apology to activists at the Gay & Lesbian Alliance Against Defamation (GLAAD).
She wrote: “I gained a lot of knowledge, and I now feel the urgency to speak out and teach others. As a lifelong LGBT ally and friend, I feel it is my duty to not only apologise for my wrong but to also correct it.
“I cannot imagine the courage it takes to live your life openly and honestly, reflecting who you truly are, or the hurt that comes from having to hide who you are because others may not support and accept you.”
She also marked International Transgender Day of Remembrance in her letter, which took place on Sunday November 20.
She wrote that “it is a day to remember those who have lost their lives due to anti-transgender violence and speak out against the fact tat transgender people face disproportionate amounts of discrimination and harassment every day.
“The lack of knowledge about transgender people contributes to the unparalleled number of violent acts against them every day.”