The force came under intense criticism after women were handcuffed and removed from crowds on Clapham Common.
A report said there was too little communication between officers at the event but their response, amid Covid restrictions, had been "measured".
It called the media coverage a "public relations disaster" for police.
Ms Everard, 33, was last seen walking home nearby on 3 March. Her body was found a week later in woodland near Ashford, Kent - prompting a public debate over women's safety.
Home Secretary Priti Patel, who commissioned the independent investigation into the force's decisions on the evening of the vigil, said she backed the police and the report had found they acted in the "right way" over the vigil.
She said there had been violence shown towards officers which was "simply unacceptable" and called for people not to "prejudge the police" based on footage because "images can be taken out of context".
Organisers of the vigil said the report was "disappointing" and said the Met will have to deal with years of trying to "regain that trust" over its policing of the event.
Her Majesty's Inspectorate of Constabulary and Fire & Rescue Services (HMICFRS) found that the force was "justified" in deciding that the risks of transmitting coronavirus "were too great to ignore" and officers "did their best to peacefully disperse the crowd".
However, it added that "there was insufficient communication between police commanders about changing events on the ground".
HMICFRS said calls for Met Police Commissioner Cressida Dick to resign - including from Liberal Democrat leader Sir Ed Davey - were "unwarranted".
A spokesman for the Lib Dems said: "We stand by our view that in the circumstances, the Met commissioner got the judgment on the vigil badly wrong."
The report said most protesters had behaved in a "dignified and respectful" way but some police, including female officers, faced abuse and hostility.
The inspectorate said "the chorus of those condemning" the force after the event showed "a distinct lack of respect for public servants facing... a sensitive and complex situation".
"It is one thing... to recognise that the scenes were worrying or upsetting (and to order an inspection such as this). It is another to jump to conclusions - and in doing so, undermine public confidence in policing - based on very limited evidence," the report said.
Whatever the official report might say about the police response, the inspectors accept that the reputation of policing in London took a big hit on Clapham Common.
Powerful images of a woman under arrest, lying beside the boots of male police officers, were quickly reproduced around the world on social media.
The inspectors say a more conciliatory approach to criticism "might have served the force's interests better" but they also note the "chorus" of what they call "unwarranted" and "uninformed" condemnation of the police from people in positions of some responsibility.
The police were wrong in their reading of the law, the report finds. Some protests can take place legally, even in areas under Tier 4 lockdown. The Met could have worked with Reclaim These Streets to manage a safe and respectful vigil. But they didn't because of "confusion" over the law.
And once again, the finger is pointed at the politicians. The report says this: "It is incumbent on the legislature to provide a set of rules that is readily capable of being accurately interpreted and applied."
If the police are largely vindicated by this report, the politicians are most certainly not.
HMICFRS said "a more conciliatory response after the event might have served the Met's interests better".
It said the events had a "materially adverse effect on public confidence in policing".
HMICFRS said its inspection involved reviewing documents and body camera video footage.
Matt Parr, who led the inspection team, said: "We found that there are some things the Met could have done better, but we saw nothing to suggest police officers acted in anything but a measured and proportionate way in challenging circumstances."
Metropolitan Police Assistant Commissioner Louisa Rolfe said officers had acted "sensibly and proportionately... given we remain in a public health crisis" and "spent considerable time engaging, explaining and encouraging before considering any enforcement action".
She said: "We welcome the considered scrutiny of this event which highlights how a snapshot may not represent the full context of the challenges police face."
Ken Marsh, chairman of the Metropolitan Police Federation, said the outcome of the report was "no surprise" - and hit out at "armchair critics".
"The knee-jerk commentary from politicians of all parties - who as the report states were reacting to a snapshot on social media rather than the facts - has made the already difficult job of our colleagues in London incredibly harder. And more dangerous," he said.
Images and footage from the resulting vigil on Clapham Common prompted widespread concern, including among the country's most prominent political figures.
Prime Minister Boris Johnson said he was "deeply concerned" by the scenes, while Labour leader Sir Keir Starmer called them "disturbing".
The Labour leader said he "remained concerned" about the events but accepted the findings of the report.
Sir Keir added it was "very important women and girls have confidence in the police".
Labour London Mayor Sadiq Khan - who called police actions "unacceptable" at the time - said he accepted the conclusions of the report.
But he said it was "clear that trust and confidence of women and girls in the police and criminal justice system is far from adequate", adding that the events had "done further damage to this".
Shaun Bailey, Conservative candidate for Mayor of London, said Mr Khan had "serious questions" to answer over his response to the policing of the demo.
In a tweet, the Labour MP for Streatham, Bell Ribeiro-Addy, suggested the report could "heighten the impression that the police are not listening to women, or respecting the right to protest".
Tensions between those who wanted to hold a vigil and police began before the evening of 13 March.
An official event had been planned by Reclaim These Streets - but the group called it off, saying police had failed to "constructively engage" on how it could be held in a Covid-secure way.
People turned up to Clapham Common despite the group asking them not to.
Reclaim These Streets said the HMICFRS report was evidence of "institutional sexism running through the force".
"We warned the Met Police... that forcing us to cancel would cause additional risk to public safety, as did Lambeth Council. They completely dismissed our warning and concerns," it said in a statement posted on Twitter.
Jamie Klingler, an organiser for the group who gave evidence to the HMICFRS, told the BBC police had "created the situation and then were left to deal with it".
She said protests were not banned under Covid laws but police had failed to provide Reclaim These Streets with the "parameters" in which to protest safely.
Police said the report had made it clear there were "good reasons" why they could not come to an agreement to allow the planned vigil to take place.
An inquest into Ms Everard's death has been adjourned until the conclusion of criminal proceedings.
PC Wayne Couzens, 48, has been charged with her murder and kidnap.
He has been remanded in custody to appear at the Old Bailey on 9 July ahead of a trial that is set to start on 25 October.