The Reds have yet to claim maximum points from five outings, despite dominating encounters with Manchester United, Sunderland and Manchester City.
However, 48-year-old ESPN analyst Barnes believes that Wednesday's 2-1 win over West Bromwich Albion in the Capital One Cup will have boosted the confidence among the squad just in time for Saturday's trip to Norwich City.
Asked whether Carrow Road provides a good opportunity for Brendan Rodgers to get his first success in the league as Liverpool manager, Barnes replied: "It is and all games are - particularly if you look at the way they've been playing.
"It's a great chance for them. The last three performances and victory over West Brom should give them a lot confidence.
"Agger being out is a big blow and Martin Kelly, but we can cover that with Jamie Carragher and other players so it shouldn't be too much of an issue.
"It's more to do with putting away the chances that they are creating."
Liverpool are currently 18th in the Premier League table.
John Barnes was speaking ahead of ESPN's live and exclusive coverage of Man United v Spurs at 4.30pm on Saturday. Visit espn.co.uk/tv for details.