The former winger believes his old side could challenge for the Premier League title next season.
The Reds have endured yet another disappointing season, currently sitting eight in the Premier League table with just 12 games remaining.
There had been some suggestions they could challenge for the title this year when Jurgen Klopp replaced Brendan Rodgers at the club earlier in the campaign.
Instead, Klopp has found life in England tougher than expected, although Liverpool are through to the final of the Capital One Cup in which they will take on Manchester City.
Barnes says that will be nice, but it is not enough and next season they could make a real attempt at winning the league.
“Winning a trophy is nice, but ultimately showing that you are consistently one of the best teams really comes from winning league performances” the former Liverpool star told the Daily Mail.
“So a trophy is a bonus. It will give the fans a bit of happiness and the young players to have won something. But that’s not enough. Next year I think Liverpool can make a much better fist of making a league title challenge.”
If Liverpool are to challenge for the title next season, much is likely to depend on the kind of business that Klopp can do in the summer.
There are several areas of his team that needs improvement based on this season, with both the defence and attack having struggled this season.
Klopp has already moved to improve the former of those with the signing of Joel Matip. If he can improve his attack as well, or more importantly keep Daniel Sturridge fit long-term, then their chances would improve drastically.