Culture Secretary Lucy Frazer told BBC's Sunday with Laura Kuenssberg the police were right to factor in the scale and global-nature of the event.
MPs, human rights groups and a former chief constable have criticised the police's tactics.
Police said on Sunday that 64 people were arrested during the Coronation.
The Metropolitan Police had previously said 52 arrests were made on Saturday. In its latest update, it said four people had been charged, while another person arrested remains in custody for non-payment of fines.
Fifty-seven people have been released on bail while two others will face no further police action.
Among those held on Saturday was the head of the anti-monarchy group Republic, Graham Smith. He was released after 16 hours in custody and said there was "no longer a right to peaceful protest in the UK".
Other concerns have been raised over reports three volunteers with a Westminster-based women's safety programme had been arrested while handing out rape alarms.
The Met said it received intelligence protesters were planning to use rape alarms to disrupt coronation proceedings.
Ms Frazer said the right to protest was "really important" and people should be heard but there had been a recent change in protesters' tactics.
Protesters have been stopping people going about their day-to-day lives, she said, and there was a need to redress that balance.
Officers would have made operational decisions on a case-by-case basis, she said, taking into account the scale of the Coronation celebrations.
"We were on the global stage, there were 200 foreign dignitaries in the UK, in London at an event, millions of people watching and hundreds of thousands of people at the scene," she added.
Labour's shadow health secretary Wes Streeting told the BBC he was reassured the Met were aware of a gap in public confidence over policing and the force was "explaining and justifying" why they made some of the arrests.
He said Labour would "wait and see" whether the force got the balance right, adding "accountability" over policing decisions was important.
Mr Streeting said if they did not get it right, it was important to "hold your hands up".
Metropolitan Police Commander Karen Findlay defended her officers' response, saying they had a duty to intervene "when protest becomes criminal and may cause serious disruption".
She added the Coronation was a "once-in-a-generation event" which was a key consideration in their assessment.
Hundreds of protesters gathered in the rain in central London on Saturday, with chants including "down with the Crown", "don't talk to the police" and "get a real job".
But Mayor of London Sadiq Khan said some of the arrests "raise questions" over the Met's actions, adding he has "sought urgent clarity" whilst investigations are ongoing.
Other protests were organised in Cardiff, Glasgow and Edinburgh. No arrests were reported outside London.
While campaigners insisted their protests were peaceful, the police said they had intelligence that groups were "determined to disrupt" the occasion.
Leader of the Liberal Democrats Sir Ed Davey said he was not sure about the exact circumstances of the arrest, and called for more detail from the police.
Speaking to the BBC's Laura Kuenssberg, he criticised the government for "passing legislation to clamp down on protest that breached British traditions of civil liberties".
Several Labour MPs have also been critical of the Met's response. Senior backbencher Sir Chris Bryant said on Twitter that "freedom of speech is the silver thread that runs through a parliamentary constitutional monarchy".
In a statement on Sunday, Republic chief Mr Smith said the arrests had "destroyed whatever trust might have existed between peaceful protesters and the Metropolitan police".
"What is the point in being open and candid with the police, working with their liaison officers and meeting senior commanders, if all their promises and undertakings turn out to be a lie?"
Mr Smith was arrested early on Saturday - before the Coronation began - at a protest in Trafalgar Square.
The Met said it had confiscated "lock-on devices" which protesters can use to secure themselves to things like railings.
It has now become illegal to prepare to lock-on following changes to the law passed this week.
But Matt Turnbull, another member of Republic who was arrested, said the straps were being used to hold the placards and had been "misconstrued" as lock-on devices.
A former police chief has said she is "very disappointed" by the arrest of protesters and strongly criticised the new powers.
Sue Sim, a former chief constable with Northumbria Police and a specialist in public order policing, said she was "very disappointed" by the arrest of protesters and called the new powers "draconian".
"I think when you're talking about terrorism, where people's lives are at risk that's a very different thing. But where you are talking about peaceful protest the whole thing for me is, what type of society do we want? We do not want a totalitarian police state," she told BBC Radio 4's World This Weekend.
Concerns about the police's approach were also raised by Westminster City Council over reports that volunteers with its Night Star women's safety programme had been detained and questioned after being stopped by officers while handing out rape alarms.
Councillor Aicha Less said the authority was working with the Met to establish what happened and was in touch with volunteers to make sure they were being supported.
The Met said it had received intelligence about plans to use rape alarms to disrupt the Coronation procession by scaring military horses, causing "significant risk to the safety of the public and the riders".
The force said three people were arrested in the Soho area of London over suspicion of conspiracy to commit public nuisance.
One man was also further arrested on suspicion of handling stolen goods. All three have since been released.
Deputy Assistant Commissioner Ade Adelekan said the force were "aware of and understand there is public concern over these arrests" and added the matter was still under investigation.