Bafana Bafana are without a win in four games in Group M and drew their latest games against Cameroon 2-2 and 0-0.
They are five points off leaders Cameroon with two games left, giving them a slim chance of playing in Gabon.
"It's most unfortunate that when the team doesn't win, the blame comes to the team," said Mashaba.
"The problem of not scoring goals doesn't start here. All the coaches in the PSL (South Africa's Premier Soccer League), when they don't win, you hear them talking about the problem of not scoring goals.
"Those are the things you can't address in the national team. You have only got three days at the most (to prepare). It must be fixed at grassroots. That where people are taught to play."
The 65-year-old believes South Africa still have a chance to make it to next year's finals, despite the odds being stacked heavily against them.
"If we win then next games we can sit on nine points and hope we can get one of the two slots for the second best teams. We are not going to throw in the towel," he said.
"Anything is possible in football. When we went to Cameron, nobody gave us a chance. Everybody said 'you are going to be hammered'.
"We fluffed it in our first two games (against Gambia and Mauritania). Possibly it was because of poor preparation or something. Those games let us down. These two games we played against Cameroon, had we won one and drawn another, we'd be talking a different story."
South Africa coach Ephraim Mashaba has insisted the team is not responsible for the poor results in their 2017 Africa Cup of Nations group qualifiers.