In a lecture for Haberdashers' Aske's city technology college, he acknowledged that higher pay for teachers is required in order to attract good graduates to the profession.
While he accepted that performance-related rewards run counter to the existing culture in schools, he said he saw no objection to those teachers that achieved more and worked harder getting greater pay increases.
However he suggested other measures needed to be taken to tackle the recruitment problem.
Mr Woodhead, recently given a new five-year contract with a 34 per cent pay increase, said it was important to reduce the administrative burden on teachers. "Targets and development plans do not raise achievement. It is only good teaching that raises standards,"he said.
In addition Mr Woodhead said morale needed to be raised: "I don't personally think that teachers see themselves as a humiliated and persecuted minority, " he said.
However, it was important to see that teachers got the praise that they deserved. Morale was not low, he said, in successful schools. He said it was currently demoralising when good teachers had to pick up the pieces left by their less competent and less committed colleagues, and who "have to cover for colleagues who have no sooner sneezed than they have gone sick".