A solitary strike by Augustine Kwem proved the difference as TS Galaxy again got the better of the Soweto giants at FNB Stadium.
A disappointed Baxter said after the final whistle that he was sure of a positive result taking into account his player's showing in training during the week.
"To sum the game up with one point I think we didn't play with the quality we have," Baxter said post-match.
"I've looked at our training this week and it's been first-class and I was certain we'd give a better performance than that.
"But when you play cup football you've got to build momentum and take the initiative and we made far too many technical errors to build that momentum.
"The more mistakes we made and the more they got hold of the ball the more they could get into our last third.
"At no time did we play consistently with the sort of quality that you need.
"That's very, very disappointing."
Chiefs face a quick turnaround with a league fixture on Tuesday away to Cape Town City.
Kick-off is at 19:30.