The 37-year-old has been discussing the Northern Irishman's precarious position.
Indeed, the Liverpool legend believes the home games will be what determine the current manager's future, with the Northern Irishman coming under increased scrutiny after failing to deliver time and again on Merseyside.
And Carragher told Sky after the Norwich draw: "With Brendan Rodgers, there was talk of him going last season. They decided to give him the benefit of the doubt. If you give him that much money and say we're going to make a change after eight league games, you should have just sacked him in the summer.
"The home games will determine it [Rodgers' future]. In their last 18 games, they've not scored more than one goal [per match] at home. That's a problem for an attacking manager who's known for creating chances."
As Opta stats show below, Liverpool have scored 19 Premier League goals at Anfield in 2015. That's worse than eight other top-flight teams and sums up why the Reds are heading for mid-table mediocrity under Rodgers.
Dominant performances at Anfield have always been a traditional part of a Liverpool season but the goals have simply dried up this year.
Admittedly, Chelsea have scored the same amount and were Premier League champions. But compare their strong defence when they won the title to the leaky Liverpool back four - scoring as many as them would never be enough under those circumstances.
As Carragher states, it's the most recent home games that have been the poorest at Anfield. And it just doesn't look like getting better any time soon unless the most needed change of all is made.