Nick Clegg said there are "questions to be asked" about how investigations into police shootings are handled after an inquest found Mark Duggan was lawfully killed despite being unarmed.
The Deputy Prime Minister said he "totally understood" the angry reaction to the finding in some quarters, but stressed the case had been considered by a jury.
Tensions appeared to have been heightened because communications between officers and local people broke down during the Independent Police Complaints Commission (IPCC) probe, he said.
The comments came as the Metropolitan Police set out to rebuild trust with London's black communities in the wake of the controversial killing - which sparked devastating riots two years ago.
Commissioner Sir Bernard Hogan-Howe will meet political representatives from the capital and prominent figures from Tottenham today to discuss how the police can improve relationships. He said he is "open to ideas and advice".
Mr Duggan's aunt Carole insisted she wanted "no more demonstrations, no more violence" - but said the "struggle" would go on for answers.
Ms Duggan told BBC Radio 4's Today programme she was not yet ready to meet Sir Bernard and the family was still in "turmoil" about the case.
"The family are still in shock right now about the result of yesterday," she said. "We are in turmoil. We don't really know what's going to happen at this point. There will be something further down the line, I'm sure."
Mr Duggan's family and friends reacted with fury after the inquest, branding police "murderers" and hurling abuse after the jury of seven women and three men gave their conclusion at the Royal Courts of Justice yesterday.
Following the verdict on the 29-year-old's death, Ms Duggan cried out "no justice, no peace" - but she insisted she was not calling for a repeat of the rioting which followed the shooting in 2011.
She told Today: "That's not what it means. In a sense it means that we will keep coming back with questions, we will keep wanting to know things, we will want answers.
"So it's that the struggle will go on peacefully but we will not give peace to the authorities until we get justice in that sense of we will keep asking questions. We will still be here for as long as it takes."
She said the Independent Police Complaints Commission (IPCC) had been "incompetent in their investigation from the beginning" and the watchdog should carry out a fresh review of the case.
"We do need to go back to the IPCC, we have a lot of questions for them. We really do need a thorough investigation. It's clear the IPCC didn't do that in the beginning. If they had done that, the jury may have come to a different conclusion."
She added: "No more demonstrations, no more violence. We will have to fight this, go through the struggle, peacefully through the right channels, to get justice for as long as it takes."
Speaking on his weekly LBC radio phone-in, Mr Clegg said: "I can totally understand and I think the commissioner is quite right to say this morning that he also understands why that has caused as much anxiety, concern, in some cases outright anger among members of the community, his family and friends.
"I am sure there are questions that need to be asked, not only about how some of these investigations are conducted.
"I fully understand, was very struck when I went there, that some of the local folk I met said part of the problem was when an IPCC investigation happens there is a whole lot of stuff that cannot be said.
"Communication breaks down about the details of the case, because it is under investigation, exactly at the moment when people need to talk to each other."
The Liberal Democrat leader went on: "At the end of the day in this case, this is a jury. This is a jury just like a court jury.
"This is a jury made up of people randomly selected just like anyone else who has been called up for jury service. It is not the police acting as judge and jury."
Mr Clegg backed a move to equip all armed police with cameras so such events are recorded.
He added: "This is really, really difficult, it is a very, very difficult time. It is a time of great anxiety in Tottenham.
"We are going to all have to work really hard that at moments of tension like this people feel their voices are heard and that disagreements play out peacefully."
Scotland Yard chief Sir Bernard said: "My sympathy is with Mr Duggan's family at the loss of their loved one, and with the communities affected by the consequences of his death.
"I welcome the verdict of a jury that our officers acted lawfully when they confronted an armed criminal who they believed posed a threat to them and to the public. But I recognise that some in the community are still angry at Mr Duggan's death.
"In particular, I know that we have much work to do with black Londoners to build trust and confidence in the Metropolitan Police.
"We know that the arguments will continue about what happened in this case. So we appeal for a balanced debate about the risks to the public from gun crime.
"My officers do not set out to run an operation that results in someone dying. They are brave people who risk their own lives to keep the public safe. Like me, they will never stop trying to reduce the risk of injury or worse. But they can only do so if we continue to have the support of all communities in London."
Firearms officers will trial the use of body-worn video cameras to record evidence and the actions of police officers to improve public confidence.
Mr Duggan was gunned down when police stopped the taxi in which he was travelling in Tottenham, north London, in August 2011.
At the culmination of the four-month inquest, the jury found that although the 29-year-old had a gun in the minicab, he most likely threw it on to a nearby grass verge as soon as the car came to a stop.
The jury's decision sparked angry scenes outside the court building, where Mr Duggan's family claimed he was "executed" and branded the judgment "perverse".
The IPCC said it was looking at new evidence that had emerged from the inquest, and the Duggan family are considering whether to try to get the inquest conclusion judicially reviewed.
Speaking of yesterday's reaction to the verdict, Hackney North and Stoke Newington MP Diane Abbott said it was important to understand the "history to that bitterness and anger" due to the relationship between police and urban communities such as the one Mr Duggan was from.
She told ITV's Daybreak: "I don't think politicians should second-guess juries, I'm not second-guessing the jury, but people have to understand how unhappy some people are about this verdict and why they're unhappy and it's because of the relationship between the police and some of the community in our urban areas.
"There's still a lot of concern about stop and search and the fact that black youth and Muslim youth get stopped and searched far more than white youth and it bears no relationship to the actual criminality.
"We just have to understand that there's a history to that bitterness and anger and there's still work to do to build the community's confidence in the police.
"You can't deal with gun crime and gang crime in London unless you have the consent of the community and that's why these sorts of issues have to be dealt with very carefully."