Mark Duggan's aunt Carole has said the family on will carry on seeking answers
The Metropolitan Police Commissioner has praised the "very dignified way" Mark Duggan's family has responded to the inquest conclusion.
On Wednesday, a jury concluded Mr Duggan was lawfully killed when he was shot dead by police in August 2011, sparking riots in many English cities.
Mark Duggan's aunt Carole Duggan said the family will fight the jury's decision "through the courts".
Sir Bernard Hogan-Howe said: "They deserve our praise".
Mr Duggan's death in Tottenham, north London, sparked widespread disorder.
The killing of the 29-year-old was followed by protests that descended into looting and rioting in the capital and spread to other cities in England.
'No violent protests'
Earlier Carole Duggan said: "No demonstrations, no more violence, we will have to fight this and go through the struggle peacefully to get justice."
Sir Bernard responded: "I praise the family in at least one respect.
"At a time of all the emotion... they thought to say to people we want to follow the legal process and we do not want violent protests.
"That's a really hard thing I think for anybody to say when you're angry about losing someone you love," he added.
Sir Bernard Hogan-Howe says the Metropolitan Police
needs to "look and feel like the people of London"
"So I think they deserve our praise for having the maturity to be able to say that and I think other people should listen to that really carefully because that's a really important thing."
After the inquest concluded, Ms Duggan took to the steps of the Royal Courts of Justice and shouted: "No justice, no peace."
She explained the slogan was about the continued fight to discover what happened to her nephew.
"We will want answers. So it is like the struggle will go on, peacefully," she said.
Ms Duggan has confirmed there are no plans at present for the family to discuss the case with police officials.
She has called for the Independent Police Complaints Commission (IPCC) to review the case.
'Reduce stop and search'
The IPCC said it was "working closely with the Duggan family solicitor to arrange an urgent family meeting" and it was hoped this would take place "in the early part of next week".
Sir Bernard said meetings with political and community leaders on Thursday had shown him the "tremendous determination there is to strengthen relationships with the Met".
"The leaders I met are committed to work hard with us to ensure that their community is not disrupted now as it was in 2011," he said.
He added the force wanted "more black Londoners amongst our neighbourhood police officers" and had "more to do to further reduce the use of stop and search".
Prime Minster David Cameron welcomed Carole Duggan's message of restraint, but stressed the outcome of the inquest had to be respected.
He said: "I very much respect Mark Duggan's aunt for saying 'pursue the case in the courts and not the street'."
Meanwhile it has emerged the names of the ten jurors who delivered the verdict are to remain confidential.
The seven women and three men, who come from the north London boroughs of Barnet, Brent, Enfield, Harrow and Haringey, have been offered counselling which is routine in cases deemed to be of a sensitive nature.
During a brief hearing at the Royal Courts of Justice on Thursday, lawyers for the family did not say whether they would challenge the conclusion.
Under the law, Mr Duggan's family have three months to bring a judicial review at the High Court, although his aunt said the four-month inquest had left them devastated.
Mark Duggan's family plans to hold a candlelit vigil for him this weekend.
The Reverend Nims Obunge, a pastor in Tottenham who knows the family, said: "It is a vigil in remembrance and respecting the life or the death of Mark Duggan.
"His family, his children, will be there and we don't expect anybody to come... to create unrest or anarchy."