Maurice Ross has publicly apologised to Notts County's Enzios Boldewijn for the "clumsy" and racially "insensitive" comment he made to the Dutch winger.
Former Rangers defender Ross says guilt prompted him to resign as County assistant on Monday after the remark during Saturday's draw at Altrincham.
He regrets that he has caused "pain, hurt and sadness" to the 28-year-old.
"I take full responsibility of it, I am not trying to hide away," Ross told BBC Scotland Sportsound.
"This is why I'm here today, not to be exonerated. I'm here to apologise to an individual who is a cracking footballer, a cracking lad. I can only say sorry."
Notts County - who announced Ross' departure on Monday - declined to comment when contacted by BBC Scotland.
Detailing the remark he made to Boldewijn, Ross said: "The exact words I said were, 'He looks like he's moving like a 40-year-old. What age is he actually? Does he have a doctored African passport?'
"I had no other intentions other than I was questioning the mobility of a footballer. When I hear it back now, I'm wincing at it.
"It was a clumsy, insensitive analogy. And it's one if I could take it back, I would. I just feel sad that I've made a really lovely boy feel bad about him myself. That's where my pain lies."
Ross, who was appointed by the National League club in March following his exit from a first-team coaching role at Motherwell, insists he is not looking for sympathy but that the "flippant" comment is not a true reflection of him as a person or coach.
"I've got foreign children," he added. "I've lived in different cultures, in Asia, in my playing career I've been to Turkey, I've integrated well with other cultures, and I just feel I've let myself down."
The 40-year-old said he "hadn't thought anything of" the incident until Monday when he was contacted by County manager Ian Burchnall.
"The manager spoke to me [again] later that day - I hadn't had any communication with the club - and he said the player was really upset and felt so uncomfortable.
"I said that on the back of that I feel I had to resign. I did it instantly."