Kelly Osbourne's feeling emotional on her first Father's Day without Ozzy Osbourne ... penning a tribute to her old man on Instagram.

The actress and television personality posted a series of photos with her dad ... photos that show her when she was just a toddler and continuing up through more recent years.

Kelly writes that she still finds herself wanting to reach out to her dad for advice or to tell a joke ... adding the ache of missing him is simply the price of loving him -- and she'd rather pay it every day then never have the honor of being his daughter.

Speaking directly to Ozzy, she writes, "I will never stop missing you. It is an honor to spend the rest of my life loving you. Until we meet again! 💔."

As you know ... Ozzy passed away in July of last year just weeks after his retirement concert. He died of a heart attack ... coronary artery disease and Parkinson's were contributing factors.

Kelly posted about Ozzy right after he died as well ... calling his passing the "hardest moment" of her life up to that point.

In more recent months, Kelly's lost a significant amount of weight ... which sources told us they believe is tied to the grief she's feeling regarding Ozzy's death.