Liverpool visit Carroll's present employers West Ham on Sunday, with the table-toppers gunning for a ninth consecutive Premier League win to continue their assault on the title.
Carroll moved to Anfield from Newcastle United for a club-record fee of £35million in January 2011 when Kenny Dalglish was Liverpool manager, but was sent to Upton Park on loan when Rodgers took over before the 2012-13 season before then making his transfer permanent last June.
"Andy wasn't let go from here because he wasn't good enough. I think he's one of the best players in Europe in how he plays, that style of attacking the ball in the air - he's outstanding," the Northern Irishman said.
"Everyone knows the way I work; it was never to say that Andy couldn't work that way, but he needed to play. He's gone on and done great for West Ham.
"Sometimes you get sucked into doing it more direct and clearly - with my history as a coach, I don't work that way."
He added: "Stewart Downing, like all the players in the opening few months when I came in, it was difficult for him. But then he really progressed and became a very important member of our team and squad by the end of the season.
"But the money that we were offered for him was going to help in getting other players in and help us continue along our journey within the philosophy."
Meanwhile, Liverpool manager director Ian Ayre has claimed there is no hurry on discussions with Rodgers over a new contract, as he wants there to be no "distractions" in the club's title challenge.
Speaking to Sky Sports, he said: "It's never been an issue. We will have our own dialogue at appropriate time, we will have that discussion. Right now isn't the time.
"We don't want a distraction. That's a private matter. I know Brendan, myself and the owners are all very comfortable with that."
