Barker remains the only coach to have won major silverware for the senior national team after winning Africa's premier competition in South Africa's own backyard.
Despite SAFA paying Brazilians Carlos Alberto Parreira and Joel Santana some big money, Bafana became the only host nation not to make it past the group stage at the 2010 World Cup.
"That side of 1996, I think they would have won the World Cup. In fact, I'm quite sure they would have," Barker tells snl24.com/kickoff.
"I think that night when they beat Ghana, they would have beaten any team in the world. With the atmosphere that was there in 2010 when Siphiwe Tshabalala scored that goal [against Mexico], there's no doubt that South Africa would have gone on and won the World Cup. No doubt about it."
Barker says he still regrets leaving the national team just before their first World Cup appearance in 1998.
"I let the team and the nation down by moving back, it was a wrong move. They were just quality players altogether and if you add the name of Benni McCarthy to that squad, it would really be a team tough to beat and certainly we wouldn't have gone down without a fight [in France]. I shouldn't have walked away from the job.
"But you know I was getting tired of it and it was difficult to win every time. But if you could see that team and you add the likes of Benni McCarthy to it, you realise what type of team you could have got. If you had those type of players in the positions that they were picked for in the African Cup of Nations, there's no doubt about it that team would have gone on and won the World Cup.
"Those players were terrific, they would have played in any condition. If you look at the midfield of John Moeti, Helman Mkhalele, Doctor Khumalo and 'Shoes' Mosheou and up front Benni McCarthy, Shaun Bartlett and Mark Williams, those are the people that could put the ball in the back of the net at the right time.
"And at the back Lucas Radebe and players like that... I have no doubt that we could have gone on and won the [1998] World Cup. The side that I left would have gone all the way to the World Cup final."
