Under questioning at the Scottish School Board Association annual conference at the weekend, Mr Peacock said the Scottish Executive was looking seriously at the issue of the low level of applications for senior management posts in schools.
Grilled by Marie Quinn, representing St Andrew's primary school board in Bearsden, Mr Peacock conceded: "It does appear that there is a post-McCrone effect here in that differentials between some of the senior positions depending on size of school mean there is less of a financial incentive in applying for a headteacher's job. We need to go and speak to potential applicants."
Mrs Quinn told Mrs Peacock that there had been only two applicants for the headship of St Andrew's primary, which she described as being in "one of the most affluent areas of Scotland and a good school".
She added: "There must be something fundamentally wrong when we are not attracting people. This (finding a good headteacher) is just so critical."
Mr Peacock told Mrs Quinn: "You are right."
He said there were still enough applicants but there was a decline and he added: "In the final analysis, whether you get five, seven or 10 applicants doesn't matter, providing they are of the right quality. We can sustain the current position but we have been clear in discussions with headteacher associations that this is an issue."
Mr Peacock was also asked by Mike Dyer, chairman of Mackie Academy school board in Aberdeenshire, whether future parent bodies would be able to influence staffing structures.
Mr Dyer said that since moving to a faculty structure Mackie Academy had lost "lots of chemistry and physics teachers". He claimed that "staff have left wholesale" because of the faculty operation.
Mr Peacock responded that statistics due out soon would show the availability of staff and how many new teachers were coming into the system this year compared to last. He added that he had just approved pound;63 million to employ extra teachers.