There was not a great deal of fortitude required on Saturday against a barely competitive Norwich side who, in losing 5-0 at Anfield, have now shipped 13 goals in their last three matches against the Merseysiders.
However, despite his advancing years, Carragher, who will be 35 a week on Monday, possesses a rare quality which Rodgers will struggle to buy in this - or any other - transfer window.
Leadership is a commodity which invariably comes with experience and, with a buying policy which is focusing on the young, Rodgers needs help from elsewhere in the short term.
The first half at Old Trafford was as insipid a 45 minutes as you are ever likely to see but, even so, Martin Skrtel will have been surprised to lose his place to the veteran centre-half - making only his second league start of the season - for the visit of a Norwich team who had taken just one point from their previous five matches.
Rodgers had no doubts about his selection, though, having this week described his team as "quiet".
"Jamie Carragher has not put a foot wrong for me since I've been here. He has been absolutely brilliant," the Reds boss said.
"He hasn't played as much as he would have liked - he's played a lot of the cup games - and I hope not to put a curse on him but I can't remember him making mistake in a game for me.
"I just felt we needed his leadership. We are a quiet team and he is a great organiser and manages the game well. He has great experience and he can play football.
"I thought him coming in would give us that bit of extra leadership and I thought he was fantastic."
Rodgers had insisted last weekend that his side did not lack the physical power to dominate midfield, highlighting the one-man force which is Steven Gerrard.
His captain put in another all-round performance, scoring his fourth goal in seven matches.
"He was absolutely incredible. The short pass, the long pass...he was magnificent," the Northern Irishman added.
"But not only that, his intensity without the ball was really aggressive and pressing. He's a captain at the moment who's playing with great responsibility and cohesion with the team, and he's really enjoying his football.
"He's happy, he's smiling and his goal was a trademark Steven Gerrard goal."
After six months, and some mixed results, other players too appear to be grasping the Rodgers concept.
In the last few weeks Stewart Downing and Jordan Henderson, both of whom appeared to have no future at the club in November, have moved up a couple of gears.
Henderson's first-time shot provided the platform from which Liverpool went on to demolish Norwich with Luis Suarez, Daniel Sturridge - who became the first Liverpool player since Ray Kennedy in 1974 to score in his first three matches - Gerrard and a Ryan Bennett own goal doing the damage.
"In terms of Jordan, he's a terrific young talent. People forget his age (22)," Rodgers said.
"He came with a big price tag and it was always just going to take him time.
"The great thing is he works his socks off every single day and you see him there: he presses, he hangs, he works, but he's also got great quality and the goal he scored is brilliant technique.
"He had to shoot with his body to produce a wonderful finish. That was the real vital goal for us because that gave us the flow then in the game and gave us that confidence to go on and push on."