Root became the latest Englishman to attack the dismissal on Tuesday, adding more fuel to the fire for what is expected to be a heated third Test at Leeds come Thursday.
In a lengthy press conference at Headingley, Root claimed England would never have appealed for that kind of stumping during his five years as Test captain.
But he saved the most direct advice for Australian players, while clearly still upset over Alex Carey dismissing Bairstow after the English batsman walked out of his crease.
"As a player it's (about) how you want to play the game, how you want to be remembered," Root said.
"And that's up to each individual.
"As a team, we want to play our cricket a certain way and want to leave a certain legacy.
"I try and put myself in that situation and position and I would like to think I would have dealt with it differently."
Root's comments come after Stuart Broad made similar remarks to Carey during play on day five at Lord's, before the quick also criticised Australia in a Daily Mail column on Tuesday.
England's reaction has prompted accusations of them being sore losers in Australia, with headlines such as "Cry Babies" and "BazBawl" splashed across tabloids.
A point Root is not overly impressed with.
"Everyone is entitled to their opinion. Everyone will see it very differently. As a player you have to play the game how you want to play it," Root said.
"It was within the rules, it was technically out. If you're happy with that, then fine.
"If you're not, I don't think you can (criticise) other people who play the game slightly differently."
Root also rejected Australia's suggestion Bairstow had attempted to stump Marnus Labuschagne in similar fashion earlier in the match at Lord's, after the Queenslander left a ball in the first innings.
"If you look at the footage, Jonny didn't gain any advantage by doing what he was doing (when batting)," Root said.
"As a batter you are fully aware when you are batting out of your crease that you are gaining an advantage.
"Whether it is covering different angles or trying to take modes of dismissal out of the game.
"(That's different to) scratching a mark at the end of the over and walking to the other end."
Despite that, Root has called for calm at Headingley this week after the ugly scenes in the Lord's long room on Sunday, with the Yorkshire crowd renowned for being one of the harshest in the country.
"Support England," he told them.
"You're coming to support your nation, it doesn't need to go beyond that. Everyone should be able to enjoy the cricket.
"Come here to support your team, do it to the best of your ability and we will play to the best of ours."
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