Chiefs were seemingly heading for another goalless draw before Khama Billiat rescued all the three points with the winner deep in virtually the last kick of the game.
"We did it the hard way you could say, they reckon every three strikes should result into a goal, so we should have been 3-0 up you could say," Baxter told SuperSport TV.
"But look you have to give the lads credit because they were working very hard, they kept their faith in what they were doing.
"The substitutes came on and had a little bit of an impact and you gotta say well done, we get into good situations, we build well, we probe well, the move is good but right into the finish, Keagan [Dolly] goes through, the keeper [Oscarine Masuluke] makes a save. I think it's a deserved win but one that from experience can go pear-shaped.
"The reason why I didn't change earlier is because I was gonna go back to a back-four but there my weapon was to get balls into the box but we had three three centre-backs and I was worried that my ambitions to win the game could resulting in us losing the game."
Baxter went on to explain why he delayed his substitutions and praised his charges for not losing their focus ahead of the Soweto derby against Orlando Pirates next weekend.
"So I waited. The second reason is that this pitch is very slick, very fast and it does take a little bit of time to get the pace of the game, so we thought we'll get more attacking players in the playing field because we just need that extra bit of quality on the transition and that extra smart pass to open up their defence. We worked very hard in on that attack and it's fitting that's what won the game for us," he said.
"And again I think the lads should get a pat on the back because traditionally the game before the derby your mind is already on the derby, so I think the concentration was good and now we can look forward to the preparations to take on Pirates," he added.