Baxter made the announcement yesterday at the Killarney Country Club in Johannesburg, ending a tenure that started in 2017.
The highlight of his second spell with Bafana was leading the team to the last eight of the Africa Cup of Nations (Afcon) in Egypt where they dramatically knocked out the hosts in the last 16.
Despite that, Baxter faced a barrage of criticism due to the football the team played which led to him believing that he wasn’t afforded the respect he deserved.
“It would be easy to say that it’s a combination (of pressure from the media, Safa and supporters) that made me resign,” Baxter said.
“But supporters’ pressure, I never feel that because if you do then you shouldn’t be in this job.
“Media pressure, that’s background noise. It’s part of the game. You guys (the media) have opinions and I don’t expect everyone to agree with my opinions.
“Respect is an important word for me, and at some point you say, at the age you are, the point in your career and life, is this what you want to be doing? If it is, you have to be getting a lot out of it.
“So, really, that plays a part to a degree but it’s not the decisive part. It’s a combination of the whole situation that I am working in.”
Baxter’s relationship with the South African Football Association (Safa) appeared strained before the Afcon as he complained about the team’s preparations for the tournament.
Safa rubbished some of his complaints by saying that they had organised friendlies but Baxter refused them.
Despite this, Safa chief executive Russell Paul paid Baxter a glowing tribute for the job he did at Bafana.
Baxter and Paul announced that the coach would not be paid any settlement amount for resigning with years still remaining in his contract.
Today the technical committee will meet to start the search for a new coach, who will continue with ‘Vision 2022’ which envisages Bafana not only qualifying for the World Cup in Qatar but also holding their own there.
“It’s been an honour to work with the South African national team,” Baxter said.
“I don’t think that anybody could have done more than I did. I’ve been in Europe to scout our young players. I have done workshops with the coaches. I have done work with the women's team and the kids (juniors). I’ve done club visits all over the country to get everyone on board.
“I hope that I have shown you guys respect when I felt that was reciprocal.
“If South Africa gets on the same page, then Vision 2022 has a massive chance to succeed. We do have resources, but we are not there yet. Tactically, mentally and socially we all have to get on the same page.
“I look forward to seeing South Africa at the World Cup.”