More than 20 officers were injured after a barrage of petrol bombs, bricks, stones and bottles were thrown at them amid "significant disorder" by both nationalist and loyalist protesters, which continued sporadically into the early hours of Friday.
Ten shots were fired from the nationalist side at Brompton Park at 12.30am.
Police fired six baton rounds and used water cannons.
Four men aged 18, 22, 24 and 41, who were arrested in connection with the disorder, have been charged with a number of public order offences. They are expected to appear before Belfast Magistrates' Court on Saturday.
Mr Baggott and Assistant Chief Constable Will Kerr gave a press conference at PSNI headquarters on Friday morning.
The Chief Constable, who described the violence as intense, praised the "superb leadership and courage" of his officers and revealed that sinister elements had tried to use the trouble as cover for attempted murder.
We have footage which shows the depth and breadth of the disorder and to some degree anarchy which took place last night, which provided cover for those more sinister elements to come out and engage in attempted murder.
Chief Constable Matt Baggott
"There is also interesting footage of the crowd fighting amongst themselves, which raises questions for me about not only the intent of those behind this to ferment disorder, but also the sheer lack of control by parents and communities," he added.
The trouble flared following a token Orange Order parade past the Ardoyne shopfronts on Thursday as part of Twelfth of July celebrations.
There was also violence in Londonderry, during which a number of petrol bombs were thrown in the Westland Street area and at the Derry Walls. One car was hit and set alight.
The return parade past the Ardoyne shopfronts was said by police to have happened peacefully and "in accordance with the Parades Commission determination".
Protests by nationalist and loyalist residents were then allowed to take place.
Nigel Dodds, of the DUP, accused the Parades Commission of making a "bizarre, crazy and mad" decision, which he said made the situation worse.
"All of it was avoidable," Mr Dodds told UTV.
"But the discredited Parades Commission absolutely messed up the situation entirely and the violence is deplorable and I wish those officers injured well.
"Our focus has got to be on working at a resolution and to get rid of the Parades Commission because without a resolution and with the Parades Commission in place it is a recipe for disaster every year."
Sinn Féin's Gerry Kelly said: "I think the difficulty was it is not all their fault, but they are the ones in the end that made the decision.
"Instead of dealing with one parade and one protest we ended up dealing with double that."
Meanwhile the Parades Commission has defended its decisions surrounding the marches and protests in the Ardoyne area.
Chairman Peter Osborne said: "There are those, albeit a small but disruptive minority, who don't understand the balance between legitimate right to parade and the legitimate right to protest without resorting to violence. They have no meaningful contribution to make in the ongoing mediation of unresolved issues over contentious parades."
The commission is consistent in saying that issues are best resolved via local dialogue.
Parades Commission Chairman Peter Osborne
"Even if parties are not able to reach a full accommodation, the channels of communication are nonetheless strengthened and a degree of trust can be established," he said.
"Common sense, open channels of communication, flexibility and a commitment to solve issues at a local level are the best way forward."
The nationalist residents' group, the Greater Ardoyne Residents Collective (GARC), was allowed to hold its protest march, which had been delayed due to safety reasons.
Around 1,500 people gathered during the GARC demonstration, as the loyalist Twaddell and Woodvale residents held a counter-protest.
A statement from Twaddell and Woodvale residents said: "The determination by the Parades Commission to allow 1,000 dissident republicans to parade along this section of the Crumlin Road and to come within yards of a Protestant community was sheer madness.
"This was not a parade but rather a dissident republican mob, who were armed with stones, billiard balls, bottles and other missiles and were intent on violence.
"Many residents in Twaddell feared for their lives and we are appalled by the folly of the Parades Commission in making their determinations and the PSNI for their handling of this dissident march."
Meanwhile GARC said: "As the head of our parade entered Brompton Park, the middle was attacked with missiles as varied as sticks, bottles, fireworks, scaffolding poles and even a set of step ladders taken from a photographer.
"We today have made history as the first people from our community to march on the front of that road and demand an end to unwanted Loyal Order Parades, and the sectarian intimidation that results from them.
"We would again, as we did in the run up to today, appeal to people not to engage in violence that will only disrupt the lives of our own people living in Ardoyne."
Justice Minister David Ford praised the PSNI for their efforts.
"The police deserve praise for the professionalism they displayed on the streets of north Belfast yesterday in the face of extreme provocation," said the Alliance minister.
"There is no justification for what happened and the actions of those involved in the rioting are to be condemned."
Brian Rea of the Policing Board condemned the disturbances across Northern Ireland.
He said: "There is no justification for the disorder which took place. I am only glad the officers' injuries are not more serious."
Secretary of State Owen Paterson said: "The localised violence that occurred in Ardoyne late yesterday remains totally inexcusable.
"While it is true that the disturbances were on a much smaller scale than in recent years it is clear that a small number of people remain stuck in the past and are intent on stoking community divisions. They will be dealt with by the full rigour of the law."
Police said investigations into the violence are continuing and further arrests are expected. They have appealed for calm.