Ruth, 60, was left devastated when Julia took her own life in June 2019 following a battle with depression.
Eamonn said Julia's death left many "unanswered questions" and said she was "tortured by mental depression".
The This Morning presenter told the Daily Star: "It’s just the unanswered questions. I experienced the sudden death of my father and there are a lot of loose ends – things where you wonder, what were your last words?"
He added: "Sudden death is a very, very difficult thing to deal with, and with Julia you know, she was just the most lovely, gentile, kind person.
"I often used to joke to her and Ruth that I got the wrong sister, but she was a lovely, lovely person – tortured by mental depression."
Eamonn said Ruth was "very caring" and "loving" to her sister, however, he thinks "there can often be a guilt when you think, 'Should I have been there? Where was I?".
Last June, Ruth shared a heartbreaking message following Julia's death.
What did Ruth say?
The Loose Women star said on social media: "My lovely sis Julia has sadly died after a very long illness.
"My heart is completely broken.
"She was the kindest and most gentle soul and I will miss her forever.
"As I am sure you will appreciate I need to take time to grieve with my family. Thank you for your understanding."
Sudden death is a very, very difficult thing to deal with.
Ruth recently admitted she almost quit her TV career after Julia died.
Speaking to Best magazine, the star said: "Following my sister Julia's death last June, I didn't feel I could ever go back to work again.
"It seemed wrong to be cheery on screen, when, inside, my heart was breaking.
"I just thought being 'happy' would be a lie - and disrespectful to my only sibling. I had no motivation or desire to be in the public eye."
Meanwhile, earlier this month, Ruth revealed a moment she saw a white feather in her garden and thought it was a sign from Julia.
What did she say?
She said on Loose Women: "I saw a white feather in the garden that was kind of stuck to the brickwork.
"I had that moment where I thought, 'Is that my sister?'
"I just had that notion because I want it to be obviously, and then I do that, 'No it’s not your sister, it’s just a birds nest in the gutter above.'"
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