Mackie sorry for racial comments
The Blades had complained about Mackie's comments made at the end of their 2-0 win at The Madejski Stadium on Saturday.
Mackie says he was caught up in the heat of the moment and did not mean to racially abuse Asaba, and he has asked for the club to fine him two weeks' wages - to be donated to the Kick Racism Out of Football Campaign.
"I would like to publicly apologise for the comment I made to Carl Asaba, which I now appreciate may have caused racial offence," said Mackie.
"I made my comment while I was still pumped up after the game during which I had a tussle with Carl.
"I deeply regret making the comment and I know I have let myself, my team-mates and the club down.
"I'm not a racist and I support the Kick Racism Out of Football Campaign and I have decided to give two weeks' wages to this campaign as a self-imposed fine."
Mackie was backed by Reading team-mate John Salako, with the winger insisting Mackie is not a racist.
"Racism is a deep hatred of a creed or a colour," said Salako. "Jon is not a racist. Political correctness is getting ridiculous."
Royals boss Alan Pardew was unhappy that the Bramall Lane outfit decided to go public on the matter before he had a chance to comment, and says he has already cleared the air with Asaba.
"We realise something had happened and I have spoken to Carl, who is a personal friend of mine," said Pardew.
"I feel it's unfortunate that Sheffield United made a statement before we had a chance to deal with it and this is not a response to what they have said."