"She has not blamed others for her problems and is growing up very quickly, albeit in the heat of the media spotlight," the 58-year-old R&B singer told Usmagazine.com.
"My father taught me to stand straight and take whatever punishment or hardships were the result of my own actions, and I am proud that I was able to hand that philosophy down to my daughter," he said.
Nicole Richie was sentenced last week to four days in jail and ordered to undergo drug and alcohol treatment. She pleaded guilty to a misdemeanor charge of driving under the influence of drugs.
She was arrested Dec. 11 for driving her sport utility vehicle the wrong way on a freeway in Burbank.
Sheriff's officials said the reality-TV star will serve her sentence at the same county jail in Lynwood that housed her "The Simple Life" co-star, Paris Hilton.
Richie has until Sept. 28 to serve her sentence.
On Tuesday, Richie told ABC News that she is four months pregnant with her first child. Her boyfriend, Good Charlotte frontman Joel Madden, is the father.
"Her pregnancy has given her a new perspective on life in general," Lionel Richie said, adding, "In spite of what has happened, I continue to love her and cherish our relationship."