Thamsanqa Gabuza struck somewhat against the run of play as Matsatsantsa clinched a win since the departure of head coach Kaitano Tembo.
After the final whistle, a number of infuriated Amakhosi supporters directed their dissatisfaction at Baxter.
"I don't have any message to the fans, because if they want me to go, I will go," an annoyed Baxter said post-match.
"If the chairman says to me 'Stuart, I don't think you are doing a good job,' then I will walk.
"I've got no problem doing that. I will walk myself if I don’t think I'm affecting the team in a positive way, I will walk. No problem."
The 68-year-old then claimed to be the only head coach to bring success to the Soweto giants in the last 20 years.
'I'm the only coach who has given this club any success over the last 20 years," Baxter added.
"I've got to go because we've dominated the game and we lost 1-0, I've got to listen to them.
"They are fans and have got the right to say exactly what they want. If that reflects what the chairman thinks, what the players think and what our majority of fans think, then maybe I should walk.
"Obviously, that's not something a group of fans will decide. The football club will decide, or I will decide and if I get that feeling, of course, I will walk.
"But at the moment, I'm looking at this as a game that we should have won. We did enough to win it, but we didn't.
"That happens in football."
