The England striker was signed by former boss Kenny Dalglish for a club-record £35million but, when the Scot was sacked in May 2012 and replaced by Rodgers, it soon became apparent he no longer fitted in.
Rodgers wanted to introduce a pressing, passing game and, while he maintains Carroll could have adapted to his methodology, the need to re-work the squad and get the big frontman's significant salary off the wage bill meant he was swiftly ushered out the door to Upton Park - initially on loan in August 2012 - before eventually completing a permanent move at a £20million loss for the Reds.
He was injured for the Hammers' 4-1 defeat at Anfield in December, but seems like to face them on Sunday on home turf.
"Andy wasn't let go from here because he wasn't good enough - I'll state that first and foremost," Rodgers said.
"He is wonderful in the air, has a good touch in and around the box, so he certainly has nothing to prove to Liverpool.
"I think he is one of the best players in Europe in how he plays - that style of attacking the ball in the air is outstanding.
"When I came in here, everyone knew the way I worked and it was never to say Andy couldn't work that way, but we had other certain financial aspects of the football club we had to look at.
"He needed to play and I think he has gone on and done great for West Ham. When he has been fit he has shown he is one of the top strikers playing in that style of football West Ham play.
"He knows he is a very good player. West Ham paid a lot of money for him and they have identified him as a top young player.
"Andy wanted to play because he had spent the 12 to 18 months beforehand not playing regularly, so this was a chance for him to do that and he has taken that really well."
Just a year after Carroll's departure, Stewart Downing followed him to Upton Park from Anfield - again at a £15million loss.
He was another player who Rodgers identified early on did not fit in with his philosophy and, although the former England winger briefly won his place back in the starting line-up midway through the manager's first season, he was let go last summer.
"I didn't want to sell Stewart," Rodgers said.
"Like all the players in the first few months, it was difficult for him when I came in but then he really progressed and became an important member of our squad by the end of the season.
"But the money we were offered for him was going to help get other players in and continue our journey along the philosophy, and unfortunately Stewart left.
"He has been one of the best - if not West Ham's best - player this season."
Against the Hammers, Rodgers is likely to name the same squad which beat Tottenham 4-0 last weekend.
However, defender Jose Enrique's season appears to be over as he is taking longer than expected to recover from a knee operation.
The Spaniard has not played since November. It was initially felt he could be back by February, but his rehabilitation is going slowly and Rodgers does not think he will feature again in this campaign.
"The likelihood is he will miss from now until the end of the season," the Reds boss said.
"The priority now is getting him fully fit and getting him ready for next season.