Police say around 100 officers have been injured since the start of the flag dispute in December.
Twenty-nine were hurt on Saturday after loyalist protestors returning from the rally at Belfast City Hall clashed with nationalist youths, amid reports of hand-to-hand fighting.
Bottles, fireworks and masonry were thrown at police lines and a number of homes were damaged during the rioting. Four police officers were taken to hospital, where one is still being treated.
Police also came under attack in the Castlereagh Street area, while a car was set on fire at the junction of Castlereagh Street and Templemore Avenue as sporadic trouble continued into the night.
Police say flag protestors were made aware that they should move out of the city centre via the Queen Elizabeth II Bridge and Middlepath Street on Saturday afternoon before they closed off the adjacent Queen's Bridge.
There are conflicting reports about how the violence began. Police said disorder broke out when loyalist protestors split off from the main demonstration.
Both Sinn Féin and the Progressive Unionist Party have criticised police tactics on the day.
"I don't think it was possible to anticipate such a large section of the crowd intent on violence would break away in such a volatile way," said the Chief Constable, who added that every return parade had previously used the Queen Elizabeth II Bridge.
"What we planned for was things that had happened before. The ownership and responsibility for that has to rest with the hundreds of people who broke away and the irresponsible behaviour of people who are organising these large scale protests."
I know for the residents who had to endure their windows being broken what a frightening and traumatic experience that must have been. I'm sorry to those residents that they went through that.
He praised his officers for bringing the breakaway group under control, but said the PSNI is set to revise its tactics.
Mr Baggott also apologised to the residents of the Short Strand whose homes had been damaged for what he called the "misery and trauma" they suffered during the attacks.
Mr Baggott also responded to police criticism that the force has not stepped in to dispel the protests which have taken place across Northern Ireland over the past six weeks, following a Belfast City Council vote to reduce the number of days when the Union flag is flown from official buildings.
Around 4,000 people took to the region's streets on Friday evening during so-called Operation Standstill and the Chief Constable said the police approach is to be "measured and responsible... [with the] right to peaceful protest upheld where possible".
"Even when the PSNI was 12,000 strong, it was not possible to take such a rigid approach towards protests," he explained.
So far 112 people have been arrested, but the police chief said many more will come as he is committed to seeing justice being done.
"There are many people currently in our footage who we are identifying and will be bringing before the courts in the near future," Mr Baggott said.
For those who remain committed to rioting and violence, I would say this. Don't make it worse because the knock on the door is coming. It is coming.
Police have done a "huge amount of evidence gathering" over the last six weeks, Mr Baggott said, and a significant number of detectives are working as part of a "thorough and prolonged investigation".
"I don't want people out on the streets adding years to the sentence that will inevitably follow for those that have taken serious disorder out into the streets," he said.
More than 30 petrol bombs were thrown in Newtownabbey and Carrickfergus on Friday night and the Chief Constable said he was saddened by the weekend of disorder, during which he had seen children as young as ten involved in disorder, their lives "being blighted by criminal gangs".
"They are areas that have been previously over the years prone to riots," he said. "There's evidence that that was manipulated by criminal gangs for their own ends to allow drug dealing and other crimes to take place.
"They were leading young people by nose towards prison.
"I don't know where their parents were, I don't know where the responsible guardians were. That's a question that they must be asked."
Mr Baggott thanked community workers on the ground involved in bringing the violence under control, and said after "a difficult weekend" it must be reasserted that politics is the only route by which grievances should be challenged.