The 19-year-old has impressed hugely since moving to Oakwell from Leicester City and has five goals to his name, just one behind top scorer Tom Bradshaw.
Against Leeds, however, Barnes was booked following a clash with Luke Ayling and then fortunate to avoid a second yellow card after rugby tackling Kalvin Phillips to the floor.
Warned by referee Andrew Madley that one more indiscretion would bring a second caution, Barnes subsequently pulled out of a tackle during the build-up to United’s second goal. He was substituted at half-time.
“You could see Leeds targeted him,” said Reds chief Heckingbottom, who admitted his side had been “second best”.
“It is appalling that he got booked for a kid (Ayling) trying to win a penalty. An appalling dive, I don’t have to see it back to know that.
“If the referee blows and books him (Ayling), Harvey doesn’t react. That put him on the back foot but, to me, it was more the reactions of their bench that put him under pressure.
“They saw him as the danger man, clearly. It is something different for him to deal with, he is going to have to learn from that.
“When you start pulling out of tackles, the referee’s influence in saying ‘one more foul and you are off’. It is difficult.”
He added: “Harvey was under pressure, which meant he daren’t make a tackle,. He pulled out of it. He has to do better there on the edge of the box.”
Heckingbottom was also unhappy with an unnamed member of United’s coaching staff, who he felt showed disrespect when celebrating Ezgjan Alioski’s goal on the stroke of half-time.
“One of their lads needs to learn how to celebrate,” said the Reds manager. “He needs to have a bit of class about him, instead of trying to get over and signal to our bench.
“He was trying to say it wasn’t at me but that doesn’t matter. You don’t do that.”