A stuttering September for the Merseyside club has included Premier League defeats at the hands of Aston Villa and West Ham, an unconvincing UEFA Champions League return against Ludogorets and a marathon League Cup third-round tie with Middlesbrough on Tuesday that eventually ended in a penalty shootout victory.
Rodgers' men have conceded seven goals in those four games to prompt criticism of some of the team's recent recruits.
Three of the back four that started last weekend's 3-1 Premier League loss at West Ham moved to Anfield in the close-season, with Javier Manquillo, Dejan Lovren and Alberto Moreno joining from Atletico Madrid, Southampton and Sevilla respectively.
Mamadou Sakho, a September 2013 signing from Paris Saint-Germain, came off the bench to replace Manquillo at Upton Park and the France international and Lovren cost a combined total of over £35 million.
And Carragher – the legendary former Liverpool defender – has been largely less than impressed by what he has seen so far from his old club in 2014-15.
"I know it's early days but, when you have spent £38m on defenders like Dejan Lovren and Mamadou Sakho, you don't want to be hearing about settling in. You want instant results but Liverpool are shipping goals," Carragher wrote in his weekly Daily Mail column.
"Lovren was brought in to add leadership at the back but Liverpool actually look worse defensively than they did last season.
"Sakho doesn't fill you with confidence when you watch him and nor does the goalkeeper, Simon Mignolet. They need to step it up urgently.
"Rodgers had the good fortune last season of injuries not making much impact on his team but, with a bigger fixture list, he had to invest to bring in numbers and quality.
"Of those who have come in only Alberto Moreno, the young Spanish left back, has impressed me so far.
"It must be emphasised it is still early days but the one thing that I associate with Rodgers’ Liverpool is absent: intensity."
