Nkhatha was consistently jeered after replacing Siphiwe Tshabalala in the 59th minute of a rainy tie at Charles Mopeli Stadium - much to Baxter's disappointment.
"The fans that braved the weather at the stadium must be commended as they cheered and supported the team. It was only a section of the fans that spoilt it," Baxter told his club's official website.
"The fans must know that if they boo players, they are transferring negative energy onto the pitch. We played good football in the second half.
"The players don’t deserve to be criticised after they put in such a gallant performance. It was difficult both on the stands and inside the pitch, but both the fans and the players gave it their all under the circumstances.
"I understand soccer is an emotional game, and sometimes criticising is what makes it the ‘game of billions’, but the criticism must be fair.
"The supporters must know that if they boo Kingston, that has a negative effect to the whole team."
Chiefs edged Ea Lla Koto 4-2 on penalties to join SuperSport United and Platinum Stars in the last-four of the competition, with Orlando Pirates and Golden Arrows contesting the remaining quarter-final on Wednesday.