Baxter quit on Friday as South Africa coach after a disappointing Africa Cup of Nations campaign in Egypt during June and July.
“I feel that I cannot continue to work with the required professionalism and passion as I have done,” the 65-year-old told a press conference at a Johannesburg sports club.
Reacting to criticism Baxter said there were “54 million national coaches in South Africa”, a reference to the 58.7 million population of the country.
Although Bafana Bafana (The Boys) stunned Cup of Nations hosts Egypt in the round of 16, they had a shameful defeat in the quarter-finals.
He is the ninth coach to quit or be fired since the Cup of Nations ended on July 19 with Algeria defeating Senegal in the final.