The midfielder admits he is lucky not to have been sacked by the club after placing what he says was "a silly bet."
Black was banned for three matches - with a further seven games suspended until the end of the season - and fined £7,500 by the Scottish Football Association last week for breaching gambling rules.
Black told RangersTV: "I need to apologise to the fans. As soon as it came out, they backed me.
"I've played a couple of games since it came out and they've been great. I'm serving my punishment now and I just hope I can come back stronger."
Black also thanked the club for backing him and giving him a second chance.
He added: "You break the rules so you've got to be fortunate to keep your job. That's where I've got to thank the board and the players and the staff who stood by me and gave me the chance.
"It's a second chance for a silly bet and it's up to me to come back stronger and repay them, as well as the supporters."