The Celtic manager was speaking in the wake of Burnley midfielder Joey Barton being banned from playing for 18 months for placing 1,260 bets on matches.
"I think what is key for players, and staff, is to lift the burden and speak about it," said Rodgers.
"For men, it can be deemed a weakness to talk about it. It's not, it's anything but."
The Scottish Football Supporters Association suggests the sport may need to "adjust its moral compass" in relation to betting, with gambling companies sponsoring the Scottish football leagues, the Scottish Cup, the League Cup, some senior clubs and the main stand at Hampden.
Rodgers said he had encountered "a number of incidents" with players with gambling problems.
"If there are problems with it with players, which I've come across, it's trying to help and educate them that there's a better way," said the Northern Irishman.
"If you lift the burden and speak about it, you'll find there are a lot of people who can help you find the solutions to it, which will help you and your family."
The Celtic manager believes, however, that a player's relationship with gambling is down to "personal responsibility".
"You have a choice," he said. "You don't have to do it. No-one's asking anyone to go and gamble. If you choose to do that, then there's a consequence."
Rodgers acknowledged that there are benefits to the game through the betting companies who "support football", adding that the businesses "provide money and do a good service somewhere along the line".
Brendan Rodgers has urged players struggling with an addiction to gambling to talk about their problems.