He acknowledged that serious mistakes were made in the investigation of Stephen's murder by a white racist gang in 1993.
Asked whether he believed there was institutional racism in the force, Deputy Assistant Commissioner Grieve told BBC Radio 4's Today programme: "There are wider issues for society here.
"We are not going to hide behind other people's racism; we will take our beating in the next couple of weeks, as we ought to do. But somebody ought to look seriously at the spiritual sickness in society."
Mr Grieve is head of the Metropolitan Police's racial and violent crimes taskforce. His readiness to accept the harsh criticisms expected in Sir William Macpherson of Cluny's report was in marked contrast to the attitude of the main police organisations, which have launched concerted attacks on the credibility of the inquiry over the past week.
The Police Federation, which represents the lower ranks, and the Police Superintendents' Association, which speaks for senior officers, accused the inquiry team of being hostile to the police and obsessed with identifying institutional racism. Federation officials claimed that the inquiry had failed to give police witnesses a fair hearing. Chief Superintendent Peter Gammon, of the Police Superintendents' Association, said it had vilified police. "Accusations of racism are still being levelled at officers involved and at the police service as a whole," Mr Gammon said last week.
Sir Paul Condon, the Commissioner, denied that there was institutional racism in the Metropolitan Police when he gave evidence to the inquiry.
Mr Grieve side-stepped the issue yesterday, saying that the inquiry had heard 15 different definitions of institutional racism. "My Commissioner has said, `Yes, we have got racism, yes, we have got racists, yes, some of our policies are downright discriminatory'," he said.
"The Commissioner's position is: what is he being asked to put his hands up to? When someone tightens up the definition for us, when someone tells us ... what concrete steps we should be taking, then we can have a look at what we are doing."
Asked for his own definition, Mr Grieve quoted a line from a poem by a black writer, Andrea Cook: "It's in the way you choose, the way we lose."
No one has been convicted of Stephen's murder, and all but one of the senior officers who carried out the investigation are now retired.
Mr Grieve, a former head of the Anti-Terrorist Branch, said lessons had been learnt from the case. His own taskforce had arrested 400 people for racially motivated crime since it was set up last July.
"We are trying to make London and indeed the country a hostile environment for racists," he said. "All of us can't spend all of our time looking back and serially apologising for what happened in the past.
"We have moved to repair the issues. We have apologised to the family. Doreen and Neville Lawrence [Stephen's parents] have done wonderful things for the country and for our communities here in London. But we have to move on. We are looking at new ways of dealing with these kinds of crimes."
Asked if he appreciated that people wanted to see the officers responsible for the mistakes in the Lawrence case brought to account, Mr Grieve replied, cryptically: "Yes, and I am looking at that now."