And he acknowledged he is fortunate to still have a career with the club following what he described as "a silly bet".
The midfielder was banned for three matches - with a further seven games suspended until the end of the season - and fined £7500 by the Scottish Football Association for breaching gambling rules.
Black said: "I need to apologise to the fans. As soon as it came out, they backed me.
"I have played a couple of games since it (the news) came out and they have been great.
"I am serving my punishment now and just hope I can come back stronger."
Black, 28, also thanked the club for backing him and giving him a second chance.
Speaking on Rangers TV, he added: "You break the rules so you've got to be fortunate to keep your job.
"That is where I have 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 is up to me to come back stronger and repay them, as well as the supporters."
The SFA sanctions were handed down after Black admitted charges of betting on three football matches on his then-registered club not to win and betting on a further 10 football matches that involved his own club.
The charges related between March 4, 2006 and July 28, 2013.
The former Inverness and Hearts player also received a warning over bets on a further 147 matches.
One of the bets was an accumulator that included Rangers to draw against East Stirling in a Third Division match last season.
He said: "I scored the goal to beat that bet, but people are saying they can't trust me and I'm this player they would have to look in the eye."
SFA rules forbid players in Scotland from betting on any match, anywhere in the world.