Bairstow had made 21 on Thursday's first day of the second Test when he was clean bowled by Siddle, with England then teetering on 171 for five.
But he was told to wait on the outfield by bowler's end umpire Kumar Dharmasena as the Sri Lankan asked replay official Tony Hill to check for a front foot no-ball.
After several minutes' study, the New Zealander decided Siddle had over-stepped, albeit fractionally.
With what had been a wicket changed into a one-run penalty for a no-ball, England's fifth wicket duo went on to add a hundred more runs before Ian Bell, who made 109, was out with the score on 271 for five.
Bairstow himself pressed on to 67 out of an England stumps total of 289 for seven.
Harris, recalled after Mitchell Starc was dropped from the Australia side that lost the first of this five-match series by just 14 runs at Trent Bridge last week, said coach Darren Lehmann and bowling coach Ali de Winter had both repeatedly emphasised the importance of avoiding no-balls.
"Ali de Winter and Darren are strict on us in the nets," said Harris, who finished the day with three wickets for 28 runs in 13 overs and not a single no-ball.
"Once we are off our long runs we are not allowed to go over. There is no excuse.
"The line is there for a reason and it is unacceptable," the 33-year-old Queensland paceman added.
As England hold the Ashes, they only have to draw this series to retain them whereas Australia need an outright win across the five Tests to regain the urn.
"It cost us a lot of runs today (Thursday) and potentially it could cost us the Ashes," added Harris of the Siddle no-ball.
"We were pretty disappointed. Darren was not very happy when we went in for lunch.
"You just can't afford to have to take 11 wickets or 12 wickets. It's as simple as that.
"It was probably the only one he (Siddle) bowled."
Indeed it was the lone no-ball Siddle delivered in what turned out to be a wicketless return of 12 overs for 48 runs.