It has been suggested, having failed to lift major silverware since 2012, that the Reds need to get back on the winners’ podium as a matter of urgency this season.
Klopp has led his side to three finals during his time at the helm, but is yet to clear that hurdle and deliver tangible success.
The German has, however, pieced together an exciting squad and Barnes believes unlocking the potential of that side in the English top flight would mean more than success in knockout competition.
The Reds legend told Express Sport: “People talk about winning trophies but they’re wrong. We could win the FA Cup by beating Swindon and Tranmere.
“You can win a trophy by not playing top teams. You can’t just win a trophy because you don’t know who you’re going to play.
“What you know in the league is who you’re going to play week-in, week-out.
“You should be able to suggest that we will be closer to the top.
“I know people talk about winning trophies as success, but I’d rather be 10 points closer to Man City and not win a trophy than win the League Cup or the Europa League and be 25 points behind City.
“Getting close to the top of the league shows how good you really are.”
Liverpool invested heavily over the summer in an effort to put themselves in contention for a first title triumph since 1990, with Barnes having been impressed by the impact made by fresh faces – despite £65 million ($84m) goalkeeper Alisson making a rare mistake during his most recent outing against Leicester.
The ex-England international added: “We knew what we were going to get with [Naby] Keita because we signed him a while ago, we knew he was coming, we knew what to expect.
“Of course, we needed to resolve the goalkeeper situation to give everyone confidence heading into the season and Alisson is a fantastic keeper.
“It’s early but they’ve fit in like they’ve been here a while.”
Liverpool topped the Premier League table heading into the international break, having taken maximum points from four games to date, and will return to action with a trip to Tottenham on September 15.