The fourth round kicks off this weekend, when the likes of Manchester City, Arsenal, Liverpool and Chelsea will look to avoid crashing out of the famous old competition as Manchester United did last month.
Barnes - who played in the 1984 final with Watford and went on to lift the trophy with Liverpool in 1989 - believes this season's competition will be viewed very differently by the teams looking to deliver some silverware.
"It maybe lost its shine four or five years ago, but now it is right back on. A few years ago it was probably the case, like when Manchester United did not even enter the FA Cup, but it is not now," said Barnes, who was in Bournemouth on Thursday to help launch the Beko Keepy-Uppy Challenge.
"The fans have let everyone know how important it is to win a cup - how much would Arsenal fans like to win the FA Cup this season?
"Clubs recognise it is a chance to win a trophy - look at what Wigan did. Roberto Martinez probably got his move (to Everton) because he had won the FA Cup.
"In the past two or three years now, you can see the big teams really do take it seriously."
Arsenal host Sky Bet League 1 side Coventry in the first of the weekend's televised ties on Friday evening, with Liverpool heading to Bournemouth for Saturday's lunchtime kick-off.
Barnes, 50, feels Brendan Rodgers' men cannot afford to switch off at the Fitness First Stadium.
"Coming to Bournemouth would not be easy for anyone, and the FA Cup will always have upsets and Liverpool have to make sure they are not one of them," the former England winger said.
"If they don't come with the right attitude and commitment, (if they) come here with complacency, then Bournemouth can beat them."
Barnes feels everything is in place at Anfield to rebuild a squad capable of launching a sustained assault on the league championship once again.
"Liverpool are currently maximising the potential they can have if they keep their key players fit, if they can add first-team players in the next season or two, then I can see them challenging," said Barnes, who made more than 400 appearances for the Reds over a 10-season spell where he helped win the league title twice.
"The way they are playing, the implementation of the strategy and policy that Brendan Rodgers likes is a good one and can show long-term consistency without having to just rely on one player."
:: Beko is the official home appliance partner of The FA Cup and is launching a national challenge to get families and communities across the UK active. The Beko 'Keepy-Uppy Challenge' is open for everyone to enter, whether as an individual, club, or school. To enter, fans simply upload a short video which showcases their skills and keepy-uppys to www.beko.co.uk/keepyuppy. Beko will make a donation to its charity partner Barnardo's for every video entry received.