Angel Lopez-Gil, 22, hit 55-year-old David Benton as Benton was crossing Skillman Avenue Sunday morning.
Benton was thrown onto the windshield of Lopez-Gil's Saturn Ion and impaled. He was dragged by the car and later died.
Instead of stopping, police said Lopez-Gil abandoned his car in a nearby neighborhood and tried to flee on foot. Officers caught up with him a few blocks away.
He was booked into the Dallas County jail and now faces felony charges.
From behind bars he told FOX 4 the accident happened on his way home from work as a server.
"I'm very sorry. There's just not enough words that I can say. I'm very, very sorry. It was an accident," he said.
He said he was not drunk. Instead he said he didn't see Benton until it was too late and then panicked.
Lopez-Gil also said he was trying to get his life back together, but didn't elaborate.
Family and friends gathered Monday afternoon at the apartment of David Benton's parents.
His father, Don, expressed no anger. Instead, he showed regret and compassion for Lopez-Gil and his family.
"I'd like for you to know that he had a big heart," said Don.
Don said his son had been battling medical problems and was looking for a job at the time of his death.
"Our feeling was that he had been in the hospital and that he was walking here to us, because he knew we'd take care of him," said Don, a minister. "And he wouldn't call me on Sunday morning to come pick him up because he knew I'd be going to preach."
Greg Clapp played soccer with Benton, who captained his high school team and won a scholarship to play at SMU.
"If you brought David's name up to a friend, I think you would instantaneously see a smile come to their face," said Clapp. "He was a great person and I'm going to miss my friend."