Brendan Rodgers looks in vain for help beyond Luis Suarez and Steven Gerrard

Elimination from the League Cup has meant there is one less front for Liverpool to fight on but their manager, Brendan Rodgers, has acknowledged he cannot keep relying on Steven Gerrard and Luis Suarez.

In an ideal world, and with a far better squad than Rodgers possesses, Liverpool's captain and their only fit senior striker would not have played 45 minutes in a vain attempt to turn the tide against Swansea on Wednesday night. Nobody at Anfield was spouting the easy clichés that this was a competition they were well rid of. Liverpool are holders of the League Cup, a trophy they have won more than any other club.

Michael Laudrup, Rodgers' successor as Swansea manager, correctly identified it as the shortest, swiftest route to the glory that fuels football.

In the home dressing room, the Liverpool keeper Brad Jones, who was almost the only member of their starting line-up to enhance his reputation, said: "The feeling we got last season going to Wembley and lifting the trophy was fantastic. It was one we wanted to replicate." In the aftermath of a comprehensive 3-1 defeat, Rodgers described his squad as "small and thin", adding that the problems would take two transfer windows to rectify.

The squad is also expensive, riddled with injuries and full of players like Stewart Downing and Jordan Henderson, who have little future at Anfield. A pair of midfielders who cost £39m have been pressed into service as full-backs in recent matches, which tells several stories.

"For this match, I looked at the young players and the fringe players and tried to give them the opportunity to get into the Premier League team," Rodgers said. "I gave the players the opportunity to come in and shine – and that is all you can do as a coach or a manager. I can't keep playing Steven Gerrard and using Luis Suarez as our only striker."

Rodgers was asked if he was not frustrated by a reliance on these two senior players in a way that would be unthinkable at Manchester United or Chelsea.

"But that is where the club is at," he said. "I would have loved to have given Gerrard and Suarez that rest because they have been played continuously and they are the catalysts for the team, but when you need them you need them.

"However, we just can't keep relying on one or two players. The ethos at Swansea, the club I have just left, is that there is no individual greater than the team. That is the ethos I want to move towards but it will take time."

Despite a beginning that in terms of raw results looks alarmingly similar to Roy Hodgson's at Anfield, the indications are that time is still on Rodgers' side.

If you exclude the detritus of the Europa League qualifiers, he has won five of his first 14 fixtures compared to Hodgson's four. Kenny Dalglish began last season with eight victories from 14.

However, Rodgers is still wrestling with Dalglish's legacy, the heavy spending on a swathe of British players whom his successor has swiftly decided are surplus to requirements.

Given the gross over-reliance on Suarez, it seems extraordinary that Rodgers has publicly ruled out recalling Andy Carroll from his loan at West Ham, despite a clause in the agreement that would enable him to do this in January.

The striker's return would at a stroke have given Liverpool a plan B and brought back a footballer whose performances in the last days of Dalglish's tenure were encouraging. However, the suspicion was always that Carroll's departure was a statement of intent by Rodgers – and these are the hardest to reverse.

Rodgers' reds rifts

The Liverpool manager has fallen out with a number of big names since arriving at Anfield:

Andy Carroll Rodgers had no hesitation in shipping £35m man out to West Ham.

Joe Cole Has been used very sparingly since return from Lille loan spell.

Stewart Downing Criticised efforts of the former Middlesbrough winger.

Jordan Henderson Yet to start a Premier League game this term and was used at right-back against Swansea.