Officers clashed with crowds gathered on Clapham Common in south London on Saturday to remember the 33-year-old marketing executive, who went missing while walking home from a friend’s flat on March 3.
Serving Metropolitan Police officer Wayne Couzens, 48, has been charged with kidnapping and murdering her.
Home Secretary Priti Patel said footage of the Clapham Common event was “upsetting” but defended restrictions on protests put in place to curb the spread of coronavirus.
In a Commons statement she added that “too many” women felt unsafe in public.
Mr Johnson was chairing a meeting of the Government’s Crime and Justice Taskforce on Monday to discuss ways to protect women and girls from violence, with Dame Cressida and Ms Patel among those attending.
Speaking ahead of the meeting, Mr Johnson said he still had confidence in Dame Cressida.
He told reporters in Coventry: “Yes I do. And what she’s asked is… that we look at what happened on Saturday night.
“The police do have a very, very difficult job. But there’s no question that the scenes that we saw were very distressing and so it is right that Tom Winsor, the inspector of constabulary, should do a full report into it.
“I think people have got to have confidence in the police and Tom’s going to look at that.”
Mr Johnson said society and the Government needed to ensure that women’s complaints about violence are properly heard.
He said “the fundamental issue that we have to address as a country, and as a society and as a Government, is that … women in particular must feel that when they make serious complaints about violence, about assault, that they are properly heard.
“We are going to make sure that that happens.”
In the Commons, Ms Patel referred to experiences shared by women in the wake of Ms Everard’s disappearance.
“Too many of us have walked home from school or work alone, only to hear footsteps uncomfortably close behind us.
“Too many of us have pretended to be on the phone to a friend to scare someone off.
“Too many of us have clutched our keys in our fist in case we need to defend ourselves and that is not OK.
“Women and girls must feel safe whilst walking our streets, that is why we have continued to take action.”
Ms Patel has asked Sir Thomas Winsor, chief inspector of constabulary, to conduct a “lessons learned” review into the policing of the vigil.
But she urged people not to “participate in large gatherings or attend protests” while coronavirus restrictions remained in force.
“The right to protest is the cornerstone of our democracy, but the Government’s duty remains to prevent more lives being lost during this pandemic.”
Calls for Dame Cressida to resign were led by Liberal Democrat leader Sir Ed Davey, while Women’s Equality Party co-founder Catherine Mayer said her position was “untenable”.
A YouGov poll of 5,168 adults indicated 47% backed Dame Cressida to remain in post, with 23% calling for her to go.
It comes as landmark legislation is brought before the Commons that will give police greater powers to crack down on disruptive protests.
Labour has said it will vote against the Police, Crime, Sentencing and Courts Bill because it contains “poorly thought-out measures to impose disproportionate controls on free expression”.
Sir Keir Starmer said the legislation did not include anything “meaningful” on protecting women and girls.
“We have got a 300-page Bill coming before Parliament, with 176 clauses of 20 schedules,” the Labour leader told reporters.
“It says lots of things about statues and almost nothing about protecting women and girls, and particularly dealing with violence against women and girls.”
But Ms Patel said Labour’s stance meant the Opposition will be voting “against measures to support victims of violent crimes, including young women and girls”.
Reclaim These Streets had organised the vigil before being forced to cancel following consultation with Scotland Yard, which said the event would be in breach of coronavirus rules.
An organiser from Reclaim These Streets said on Monday she did not want Dame Cressida to resign, but asked for the police chief to meet the group.
Anna Birley told ITV’s Good Morning Britain: “We are a movement of women seeking to support and empower other women, and as one of the most senior women in British policing history, we do not want to add to the pile-on.”
The Metropolitan Police Commissioner said what had happened to Ms Everard made her “more determined, not less” to lead the organisation, as she resisted calls to quit over the events.
Four people were arrested for public order and coronavirus regulation breaches at the Clapham Common event on Saturday, the Met said.
Hundreds of women have left floral tributes in the park near to the route where Ms Everard walked.
Throughout Monday, mourners arrived from across the capital to leave flowers and cards on the bandstand at Clapham Common.