The Reds have won just two of their first four games of the new Barclays Premier League campaign and sit six points behind leading duo Chelsea and Tottenham.
But Barnes, now manager of neighbours Tranmere, says: "It's ridiculous to write off Liverpool. Look at the start Manchester United had last season and they went on to win it."
He added: "The Liverpool players and fans should have a belief that they can be competitive and can go all the way.
"They went very close last season, and although that doesn't mean they're going to do it this year, it will give them belief that they can win it - regardless of the start they've had.
"Maybe two years ago a start like this would have knocked Liverpool, but they now have real belief.
"If they stick together, have the right spirit, desire and discipline - as they do - and a togetherness, then they'll be there come the end of the season."
Meanwhile, Dutch international Ryan Babel believes a loan spell at Ajax in the second half of the season will help his chances of playing in the World Cup finals next summer.
The winger was initially axed from the Holland squad ahead of the weekend game with Japan and next week's World Cup qualifier with Scotland, but recalled this week due to injuries.
He said: "I was told(by Liverpool) I would play more minutes and have more chances, but after the first defeat I lost my place. I think half a season at Ajax with a view to the World Cup would not be a bad idea."