Sir Ian said the Met had "worked tirelessly" to improve its procedures
The commissioner of the Metropolitan Police has said the force must show "humility" over the shooting of Jean Charles de Menezes.
In a leaked memo to staff, Sir Ian Blair said procedures had "failed" on that day and the Met took "full responsibility" for what happened.
He insisted that lessons had been learned, adding: "No-one set out with any intent to let a young man die."
The inquest into the Brazilian's death in 2005 has begun in London.
Mr de Menezes was shot dead at Stockwell Underground station in south London after being mistaken for a suicide bomber.
The internal address by Sir Ian was leaked to group Justice 4 Jean which has campaigned for the police officers involved in the incident to be prosecuted.
In the memo, Sir Ian told staff how he wanted the Met's counsel to behave at the inquest.
"Our approach will be one of humility," he wrote.
"On 22 July 2005, we confidently believed that our systems of command, of surveillance and of firearms intervention were among the best in the world.
"However, they failed in response to a previously unforeseen circumstance, suicide bombers on the run.
"Jean Charles de Menezes was an entirely innocent man and the Metropolitan Police takes full responsibility for his death."
The police officers who shot Mr de Menezes will appear anonymously at the inquest at the Oval Cricket Ground.
Sir Ian made reference to them in his memo: "The officers involved will be giving evidence of doing what they did with good intention.
"They have my support and should have yours."
In 2007, the Metropolitan Police was found guilty of breaching health and safety laws over the shooting of Mr de Menezes.
But the commissioner said he believed the inquest - rather than that Old Bailey trial - was the right place "for holding us to account".
Sir Ian said many people in the Met had "worked tirelessly" since the incident to improve procedures.
"For instance, many of you may be aware that we have upgraded our control room which deals with fast-moving, life-threatening incidents and that we are creating a unified surveillance command," he said.
"It is to be hoped that one of the legacies of Jean Charles is a Metropolitan Police Service even better equipped to deal with tragedy and danger."
Sir Ian said the inquest would be "the most testing tribunal" the Met had faced since the Macpherson Inquiry in the 1990s concluded it was guilty of institutional racism.
He also said it came at a time when there were other "serious challenges" for the force, notably the race discrimination case being brought by Assistant Commissioner Tarique Ghaffur.
A spokesman for the Met confirmed the leaked memo was genuine, but said it was not unusual for the commissioner to make addresses of this nature.