Barry was given the captain's armband for England to face Ghana last week but Barton has offered a damning assessment of the City player.
"Did you see the game against Germany at the World Cup?. If you watch the fourth goal, when [Mesut] Oezil was up against Barry, it was like the hare and the tortoise," he told French magazine So Foot.
"Barry's got a very good agent. He's also discreet and always agrees with the manager. He's like the guy who sits in the front row and listens to the teacher. I certainly don't lose any sleep when I play against him."
Barton also staked his claim for being the best English midfielder currently playing in the Premier League.
He said: "Honestly, I think I'm the best [English midfielder]. Luka Modric and Samir Nasri are very good, but in terms of English players... well, Jack Wilshere isn't bad, but Frank Lampard's on the way down and Steven Gerrard's been injured a lot."
The Newcastle man also slammed the FA for refusing to adapt to the modern game.
He said: "France killed us at Wembley. We English will play the next 50 World Cups and we'll never win one.
"The people in charge at the FA played football maybe 50 or 60 years ago and still think that we can win a World Cup in the same way we did in 1966.
"We're too focused on tradition in England, like always having to play 4-4-2. Sometimes you need to experiment, drop a bit deeper so you have more space to move into. France, Italy and Germany have done it. We've been doing the same thing for 20 years."
However, regardless of his thoughts on the England national team, Barton admitted that he would be keen to join up with Fabio Capello's side.
He said: "I'm English and I love playing for my country. Maybe the people at the top have a problem with me. I don't know. But the trouble I had was four years ago. They should be able to forgive, shouldn't they?"
The former Manchester City man also outlined his concerns over the future of current club Newcastle, but has insisted that he would be willing to sign a new deal, as long as team-mate Kevin Nolan does the same.
"We had a good player, [Andy] Carroll, and we sold him. I told the management that I was worried, that I was scared this might happen every year. But they assured me they don't want to go down that road," he added."If Nolan signs a new deal, I will as well. But I hope the club step things up. I want to be ambitious and I think the club share that desire."