Australia wicketkeeper Alex Carey under-armed the ball at the stumps after Bairstow left his crease at the end of an over, triggering long and loud booing from the crowd. Australian players were also verbally abused by MCC members in the stadium's Long Room.
The visitors, who won at Lord's by 43 runs, hold a 2-0 lead in the five-test series against England.
"What amazed me, and what I told the Australians I could not believe as we left the field at lunch, was that not one senior player among them... questioned what they had done," Broad wrote in his Daily Mail column on Monday.
"Ultimately, (Australia captain) Pat Cummins is a really great guy and I would be amazed, once the emotion settles, if he does not sit back and think, 'I got that one wrong', even though his bottom line at the time was winning a test match.
"The Lord's crowd are obviously huge cricket lovers and never before have I seen such a reaction from them like that."
Broad also referenced Australia's on-field culture change instilled by Cummins and the contrast to the attitude before the infamous 2018 ball-tampering episode in South Africa.
"I was angered by Australia's decision, particularly having heard their lines about creating a new legacy as a team, and how they have changed since the tour of South Africa in 2018," Broad said.
"I just said to Pat on repeat: 'All these boos are for you, for your decision'. And: 'What a great opportunity you had to think clearly.'
"To Alex Carey, I said: 'This is what you'll be remembered for, and that's such a shame'."
