The clash, which was played on Thursday, 5 August at the Mane Garrincha Stadium in Brasilia, ended in a goalless draw.
Mvala received his marching orders in the 58th minute following a second yellow card, leaving his compatriots to battle it out against a strong Brazil side for just over half an hour.
“I feel really bad for getting a red card and I feel as though I made a big mistake which was unnecessary, but I had to do something in the situation,” Mvala said. “I want to apologise to my teammates and the country as a whole, as I may have disappointed a lot of people. I believe I have learnt a lot from that mistake.”
Mvala, who will now serve a one-match suspension, went on to heap praise on his teammates for applying themselves despite the one man disadvantage.
“I also want to applaud my teammates for their courageous performance after my departure,” he said. “We played really well, and they continued even during my absence. They did extremely well, and I just believe had it not been for my error maybe we could have attacked more instead of being defensive for the last 30 minutes.
“It was very difficult, but they pulled it off.”
South Africa faces Denmark on Sunday, 7 August with kick-off at midnight South African time.