Eddie Jones was reprimanded by the Rugby Football Union for his criticism of the national team's reliance on private schools.
Jones, 62, claimed the pathway produced players who had enjoyed a "closeted life" and lacked "resolve" in a weekend interview with the i newspaper.
The England team that won the Test decider in Australia were fully or partially schooled.
The RFU said that Jones was reminded of the sector's value.
The RFU supports the role state and independent schools play in introducing boys and girls to rugby.
Strong partnerships within the education sector ensure that players are supported and offered opportunities to develop at all schools.
The most recent England men's squad contained players who have benefited from time within independent schools, including Maro Itoje and Henry Arundell.
We are always trying to broaden the appeal and accessibility of rugby union to boys and girls from a wide range of background.
Bill Sweeney, the union's CEO, spoke to the Australian head coach about his comments.
The system yielded young players who struggled to lead because "everything's done for you", according to Jones.
We are the best in the world when we are on the front foot. Our resolve is not as it should be when we are not on the front foot.
Sir Clive Woodward, the head coach of the 2003 World Cup winning squad, labelled Jones' criticism "insulting, divisive and disrespectful".
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