A total of 96 people have now been arrested since the trouble began in December, when City Council voted to reduce the number of days the Union flag flies at City Hall.
Police came under attack for a fourth consecutive night on Sunday as they dealt with disorder in the Castlereagh Street, Albertbridge Road, Beersbridge Road, and Mountpottinger Road areas.
The Chief Constable said there is "no excuse" for the violence, which has led to 62 officers being injured.
Mr Baggott said: "Senior members of the UVF in east Belfast as individuals have been increasingly orchestrating some of this violence.
"That is utterly unacceptable and is being done for their own selfish motives."
Seventy-three people have been charged in connection with the trouble.
Five have been reported to the Public Prosecution Service, 17 have been released on bail and one person has been de-arrested, police said.
It is understood children as young as 10 have been involved in the trouble.
At the moment there is a lack of control, which for me is very worrying.
Matt Baggott said the PSNI has the resources to deal with the situation at present, but warned that it could undermine his ability to tackle dissidents in the long term.
"I would like everybody involved in these protests now to take a step back," he continued.
"My ambition is that the protests will come to an end, although you appreciate that the police are not in control of that.
"But if not, at the very least those involved in the protests should be off the road, not causing obstruction, absolutely condemning violence and ensuring that these young people are not involved.
"And that requires a concerted effort from politicians and those who have put themselves up as organisers acting together and from parents and responsible members of the community."
PUP leader Billy Hutchinson met with Mr Baggott on Sunday following allegations of police heavy-handedness - which the PSNI chief has rejected.
Mr Hutchinson called on those involved in the UVF to desist from protests.
"What we need to be clear about is that he's talking about from Friday night, he's not talking about previous to that where other people have been saying this," he told UTV.
"I got a similar analysis yesterday and what I am saying now is that I am asking people involved in the UVF in east Belfast if they are involved to desist - let's give the protest back to the people and allow the people to have peaceful protests."
The bill for the ongoing policing operation is thought to be around £4m so far.
The trouble started last month following Belfast City Council's vote to limit the number of days the union flag is displayed at City Hall.
On Monday night, the council met for the first time since the flag controversy erupted.
Meanwhile, Fianna Fáil's Justice Spokesman has called for a flag protest, which is planned in Dublin city centre on Saturday, to be called off.
Niall Collins TD said: "I respect everyone's right to engage in peaceful protest. However, I believe that Willie Frazer's stated intention to take three busloads of loyalist protesters to Dublin this weekend is ill-judged and I would call on him to rethink the plan."