The 75-year-old remains the only coach to win the Africa Cup of Nations (Afcon) title with Bafana Bafana, doing so in 1996.
The Southern African giants were eliminated from the 2019 Afcon in the quarter-finals in Egypt and Barker feels the team needs to improve.
"We are a big country, we shouldn’t play catch up. We are not producing top players in Africa at the moment."
Barker believes Bafana can only win trophies if the players are allowed to express themselves on the field.
"When I saw them playing at the Afcon, I asked myself, is that the way we’re supposed to play? The coach (Stuart Baxter) had a big influence on how we played and he didn’t get it right," he added.
“We are capable of going back to dizzy heights. I’ve stayed out of the selection of coaches in the last couple of years because I know how difficult it is.
"There’s definitely a huge room for improvement. We’ve got to be a successful football nation,” the legendary South African coach explained.
Bafana have a new coach in local tactician Molefi Ntseki having replaced British mentor Stuart Baxter, who resigned early last month.
Barker has adviced Ntseki to allow the players to play with flair with the team set to take part in the 2021 Afcon qualifiers.
“Molefi needs to get his team playing with freedom. He must let them have a full go, he must let them express themselves. It is part and parcel of the game," he said.
"We like the flair. We like controlling our destiny. I think it is very important that we play ‘off-the-cuff’. If we play like that, we will win a lot of things."
South Africa will be away to Ghana in their opening 2021 Afcon qualifier (Group C) on the 11th of November 2019.
Before facing Ghana, Bafana will take on Mali in the Nelson Mandela Challenge in Port Elizabeth on October 13.