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 £7,500 by the Scottish Football Association last week for breaching gambling rules.
Black claims gambling is still taking place within the Scottish game but insists he would not like to see another player punished like himself.
He 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."
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 to the period between March 4, 2006 and July 28, 2013.
The former Inverness and Hearts player also recieved a warning over bets on a further 147 football matches.
One of the bets was an accumulator which included Rangers to draw against East Stirling in a Third Division match last season.
He said: "Looking back, I wasn't thinking at all. A small bet of £5, there was obviously no thought in it.
"It was a silly bet and I'm paying for it now.
"I scored the goal to beat that bet but people are saying they can't trust me and I'm this player they'd have to look in the eye.
"People who know me, and supporters who watch me every week, know that I give 100 per cent in every game, even in training."
The SFA operates a zero tolerance approach, which restricts players from betting on any match, anywhere in the world.
Black said: "I broke the rule and deserved the punishment. I shouldn't have done it.
"There are a lot of players out there who are still doing it. I could sit and name players but I'm not going to do that.
"I'd certainly not like to see any players in Scottish football getting done for breaking the rule like I did.
"It's affected me off the pitch, people judging me."
Black says his family life has also been affected.
He added: "It was horrible. I had reporters knocking on the door, with my daughter sitting in the house, and I'm trying to keep it away from her.
"I'm playing at a big club and it was hard for her and my other half as well.
"I put my hands up. It was a mistake and I'm serving my ban and my punishment for it."