According to Birkhead, he moved to Kentucky with his daughter following Smith's death in 2007 in order to avoid the spotlight.
"It takes away the chase, it takes away the curiosity, it takes away the false stories," he said.
Birkhead also believes Smith would be pleased with how he is raising their daughter.
"Other that I don't dress her in pink every day, I think she'd would probably think I'm doing a pretty good job,'' the 43-year-old said.
"I'm not the best dad, I have my faults, but I do the best I can with what the situation is. We make the best of it, and I think Dannielynn's best days are still to come. She's got such a bright future in front of her, and I try every day to keep a little bit of the memory alive of her mom."
Danielynn was five months old when Smith died in 2007 after accidentally overdosing on prescription drugs.
Birkhead obtained full custody of his daughter after taking a DNA test to prove his paternity.
In July, Birkhead appeared on "The Steve Harvey Show" where he discussed what his daughter knows about her mother.
"She knows that her mom was famous," Birkhead replied, "and that people want to know about her, so, it's different for her, my daughter, because it's nothing for her to go past a story in the check-out stands, on the cover of magazines of her mom or herself or us or whatever and it's a little different from your normal situation."
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