The striker had one year remaining on his contract when Rodgers took over at Liverpool in 2012, but opted to move to his hometown club, helping them secure promotion to the Premier League last season.
The manager told the club's website: "It's one of my only regrets, really, that I never got the chance to work with Craig. I've followed him in his career right the way through; an outstanding player, very honest, speaks his mind, but is an ultimate professional.
"When I came in, he had a year left on his contract but for other reasons he needed to move back home, and that was a regret because I've always seen him from the outside as someone who was very passionate about football, but who had great qualities.
"So for me to lose a player of that quality when I did was obviously very disappointing, but I respected his opinion at the time. He went back to his home in Cardiff and has been a real iconic figure for Cardiff."
Liverpool face Cardiff this weekend.