Notts County assistant head coach Maurice Ross resigned after allegations that he made a racially insensitive comment to one of his players.
Ross, who was appointed in March, left on Monday following the incident in Saturday's draw at Altrincham.
The ex-Rangers defender apologised and called the remark "unacceptable".
"I made an ill-judged comment to a member of our playing staff which has led to my departure from the club," the 40-year-old said in a statement.
"I would like to place on record my apologies to the player.
"While it was said in the heat of the moment with no malice intended, it was nevertheless unacceptable and I'm devastated by the impact it's caused."
On Monday Notts County said the former Wolves and Millwall right-back had left the National League side with immediate effect.
The club have not yet commented on the reasons behind his departure.
County's captain Michael Doyle has agreed to assist manager Ian Burchnall with coaching duties until the end of the 2020-21 season.
The Magpies are 10th in the National League, four points off the play-offs, having not won in their past eight fixtures.