Rodgers was appointed Anfield boss following an impressive spell at Swansea City, securing promotion form the Championship in his first season at the Liberty Stadium before guiding the club to a mid-table finish in the top-flight.
Contrastingly, Liverpool had a disappointing season, finishing eighth, a record low for the Merseyside club in the Premier League era. However, the former Reds winger believes that the club's performance in cup competitions was encouraging and is adamant that there will be an improvement.
He told Press Association Sport: "Improvement - we will finish better than eighth."
|2/1||Liverpool are 2/1 with PaddyPower to achieve a top-four finish in the 2012-13 Premier League|
"Brendan Rodgers is there now and I urge all the fans to get behind him, support him, believe in him and see where it takes us.
"I don't think we are necessarily strong enough to win the league but we should be looking to finish between fourth and sixth, and if we could get into fourth spot, that would be a great achievement."
|"I don't think we are strong enough to win the league but we should be looking to finish between fourth and sixth"
- John Barnes
"We have to be realistic and we have to trust the manager - know his philosophy and know he will bring in the players to suit that philosophy," he added.
"They might not be names we have heard of - like Gylfi Sigurdsson; when he came in [at Swansea] no-one thought anything much of him, but you can see what he did.
"He is not coming to Liverpool, but if he [Rodgers] signs a player we have not heard of that he knows can fit into his philosophy and pattern, then we should support that, rather than saying 'unless we get big-name signings, we are not going to be optimistic'."