The 23-year-old has struggled to justify his £35m price tag since joining the Reds from Newcastle United in January 2011.
Carroll has managed just 11 goals in 56 appearances and former Reds boss Kenny Dalglish largely used the imposing forward as an impact substitute last season.
Rodgers replaced Dalglish as Liverpool’s new manager in May, prompting Carroll’s future at the Merseyside outfit to be cast in doubt, with the former Swansea City boss preferring a possession-based style of football.
Newcastle manager Alan Pardew revealed last week that the Magpies were interested in bringing Carroll back to St James’ Park, but Rodgers backed the striker to succeed at Anfield.
“Andy is a terrific young player,” Rodgers said. “I had a brief chat with all the lads and over the next couple of weeks I’ll be able to speak to them with more confidence and on a one to one basis.
“There is no doubt he is a terrific talent. There has been a lot of unfair criticism aimed towards Andy.
“He is a player who can play in a number of styles and it was a wee bit unfair on him [for people] to say he couldn’t fit into the way I would want to play.
“For me, your game is based on your players, the players you have. I am here to win games.
“We’ve got a number of very, very talented players in the group, of which Andy is one.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news