Australia wicketkeeper Alex Carey underarmed the ball at the stumps after Bairstow had left his crease at the end of an over on the final day of the second test, which Australia won by 43 runs to go 2-0 up in the five-match series.
The atmosphere at the ground quickly turned hostile towards Australia's players after the dismissal, which is legal but perceived by many as against the spirit of the game.
Pat Cummins' side were also were also verbally abused by MCC members at Lord's, and Root said there was a line that should not be crossed.
"Support England," he said. "I think that's the most important thing, that you come in to support your nation, doesn't need to go beyond that.
"It shouldn't ever go beyond that."
Root expected wicketkeeper-batsman Bairstow would be fired up for the third test.
"Jonny thrives off things like this," Root said.
"I'm sure he will want to entertain the local crowd. I think it is set up nicely for him, but you have still got to go and do it."
"I don't think he took it great. I don't think anyone would they?
"He felt a bit hard done by. I don't think anyone will be leaving their crease (this week)."
