Mr Robinson condemned the violent attacks during which 29 police officers were injured in east Belfast and homes in the nationalist Short Strand area were damaged on Saturday.
Trouble flared on the Albertbridge Road when loyalist protestors returning from a mostly peaceful rally at Belfast City Hall clashed with nationalist youths.
It was the latest in a series of protests held by loyalists after Belfast City Council voted last month to restrict the flying of the Union flag over City Hall to 18 designated days.
"There are political issues and people that feel disengaged and people that feel if we are trying to build a shared future they are not getting their share," the DUP leader told the Andrew Marr Show on Sunday.
It is no accident that the violence is occurring predominantly in those areas that are considered to be suffering from deprivation.
The decision to limit the flying of the Union flag was supported by the Alliance Party, Sinn Féin and the SDLP, and Mr Robinson said he believed it was a "bad" move.
"It was a bad decision but the only way of addressing the bad decision is through the democratic process," he said.
Mr Robinson, along with deputy First Minister Martin McGuinness, is due to meet with the Tánaiste Eamon Gilmore and NI Secretary of State Theresa Villiers next week to discuss the flag dispute.
Mr Gilmore, who is also the Irish Minister for Foreign Affairs, said the violence is being orchestrated.
"Those behind it are known criminals, intent on creating chaos.
"This has nothing to do with real issues around flags and identity in a shared society which are the subject of intensive political discussions at present," he said.
Sinn Féin President Gerry Adams visited homes in the Short Strand area on Sunday.
He said residents feel let down by the police and called for politicians to stand up to sectarianism.
"The people of the Short Strand would not have a lot of confidence in the PSNI to start with, but what they do have is a certain faith that things will get better," he said.
Mr Adams said the violence that took place on Saturday was orchestrated and "part of a deliberate policy of coming to these so-called interface areas and attacking people only on the basis that they are Catholic".
"The people of the Short Strand were not out rioting. The people of the Short Strand were not out hijacking. The people of the Short Strand were not out wearing balaclavas and hoods. The people of the Short Strand were not attacking the PSNI. The people of the Short Strand were involved in no activity at all," he claimed.
We will not tackle sectarianism by running away from it. We have to face up to it. We have to stand full square against what is happening.
Police said missiles were thrown by "rival factions" at the flashpoint during Saturday's disorder.
In total, 99 officers have been injured in five weeks of rioting across Northern Ireland, with much of the unrest concentrated on east Belfast.
So far police say 110 arrests have been made, with 84 charged, eight reported to the Public Prosecution Service, 17 released on bail and one adult cautioned.
A 32-year-old woman has been charged with disorderly behaviour and obstructing a constable in connection with the disorder in Castlereagh Street on Saturday.
She is due to appear at Belfast Magistrates' Court on Monday.
Last week unionist representatives gathered at Parliament Buildings to discuss issues of concern to loyalists, during the first meeting of the newly-formed Unionist Forum.
Ulster Unionist leader Mike Nesbitt said the forum "offered a positive alternative" to the disorder.
"Street violence from so-called unionists, no matter what age, advances nothing but the cause of Irish nationalism. It is high time those involved in rioting realised they are destroying the very cause the hope to promote."
But politicians from other parties have called for more cross-community talks to dispel tensions.
East Belfast Alliance MLA Judith Cochrane said people are angry at the disruption.
"This violence has shown the deep rooted divisions that still exist in our society. We must see action to deliver a truly shared future.
"This can only be done through working together to seek shared solutions, not through the establishment of groups which seek to exclude those whose viewpoint may differ from yours."
A second peace rally was held at Belfast City Hall, where campaigners made five minutes of noise in opposition to the violent outbreaks on Sunday.