Victor Letsoalo netted a brace for Thwihli Thwahla, scoring in either half before Sfiso Hlanti pulled a goal back for Chiefs in the last 14 minutes.
However, Amakhosi capitulated in the closing stages, as an own goal by Sibusiso Mabiliso and a stoppage time goal by Mfundo Thikazi gave Royal an emphatic win.
"I think it's not only a hard defeat, it's an embarrassment. I think the first 20 minutes of the game we picked up where we left off [against Sundowns]," Baxter told SuperSport TV.
"The structure was good, the passing was good, we created a couple of chances but give away a silly goal again, the we chased the game, we have to chase the game.
"The naivety of the players as the game went on was astounding really and we never really looked like getting back into it
"You know we get a goal back, 2-1, we've changed about four different positions, then you lose a little bit of cohesion and you hoping you get fresh legs but we never really looked... our naivety again when we gave away the last couple of goals, when we were chasing the game.
"It's not good enough and it's embarrassing and I apologize to the supporters," the former Bafana Bafana coach went on.
"We're back to the same old... I thought for the first 30 minutes it was, we lost it towards the end of the first half because we started to chase the game but we had chances to score and put the game in a better position for us to play.
"But we don't, we're inviting them into the game, we're making very naive decisions and that takes the game over to them and then we have to chase it."
Baxter was asked to explain the reason behind bringing on Anthony Akumu late in the first stanza for the injured Phathutshedzo Nange and other substitutions in the second stanza.
"When Nange goes off it's a difficult one for us, Anthony goes on he's more a defensive player, not a creative player, so we think if he sits a lite bit we'll push Cole [Alexander] on," he said.
"And then it's a question of making substitution as you go along you know. I really felt the players we had on the field were the ones that could do the job better but fresh legs, a new impetus, for someone to change it, a tactical change.
"But in terms of tactical changes we lost our balance, maybe I should take the responsibility for that but I think, you know our players are good enough to be able to react to that. But the way we reacted, with the naivety, it wasn't great."