The court heard that their victims were stamped on, forced to strip and hit with bricks.
Sentencing the brothers, the judge Mr Justice Keith described their behaviour as "appalling and terrible".
After the sentencing, a summary of a serious case review by Doncaster Safeguarding Children Board was released.
Board chairman Roger Thompson said the case was "preventable" and "many important lessons" needed to be learned.
Mr Jarman said that when he took over the role of director of children's services last April the organisation was "totally broken".
He said: "I would like to start by offering an unqualified apology on behalf of Doncaster Council for the admitted failings which led to this terrible incident.
"In particular, I would like to apologise to the victim of this case and their families and offer my apologies also to the residents of Doncaster."
Mr Jarman said: "Where people are seen to be culpable... action will be taken against them."
He confirmed that only one person had faced disciplinary action so far as a result of this case.
Asked if he thought that was "astonishing", he said: "I don't think it's astonishing at all.
The findings of the report follow what has undoubtedly been an exceptionally shocking crime
Roger Thompson, Doncaster Safeguarding Children Board chair
"Now that the serious case review has been published, we will appoint an independent investigating officer who will look into these matters without fear or favour," he said.
"Where people are seen to be culpable, as appropriate, action will be taken against them of a disciplinary nature.
"Where people have left the organisation, but are equally assured to be responsible for this, we shall have no hesitation in reporting them to their professional bodies.
"I think it would be irresponsible not to do so."
Roger Thompson, chairman of the Doncaster Safeguarding Children Board, said: "The findings of the report follow what has undoubtedly been an exceptionally shocking crime committed on two innocent young boys.
"On behalf of the board, I would like to express that our thoughts are with them and their families as they continue with their recovery.
"No-one could have predicted the severity of the attack.
"However, the review has concluded there were serious failings in local services, and the executive summary report has indicated that the assault was a preventable incident."
He said the review had made 18 recommendations for improving practice and procedure, many of which have already been actively addressed.
He said the board was "very concerned" that contents of the serious case review were disclosed to the news media before official publication of the executive summary and this was now subject to a police investigation.
"We are aware there is a widespread debate for the Doncaster Safeguarding Children Board to publish the serious case review in full," said Mr Thompson.
"The board is following government practice by publishing the executive summary report only to protect the families involved.
"If government policy changes then the Doncaster Safeguarding Children Board will follow that guidance."
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