The DUP leader was speaking after further trouble erupted in east Belfast over the weekend, linked to the dispute over the flying of the Union flag.
"This issue will never be solved on the streets but only through democratic means," Mr Robinson told the Assembly on Monday.
"You do not respect a Union flag if you are using it as a weapon to charge against someone. You are not showing respect for the Union flag if you need to wear a mask when carrying it."
Saturday saw 29 police officers injured amid "heavy and sustained attacks" which broke out after loyalists and nationalists clashed at the Short Strand interface, following a protest in city centre. Police also came under attack in the Castlereagh Street area.
It is the ballot box that will decide Northern Ireland's political direction. Those who are engaged in violence on the streets are not friends of Unionism, they are the enemies of democracy
On Friday, more than 33 petrol bombs were thrown at the PSNI amid serious disorder in Carrickfergus and Newtownabbey.
It comes after Belfast City Council started flying the Union flag only on designated days at City Hall following a vote in December.
Mr Robinson continued: "We rightly condemn the violence that has taken place but, we must also set out a political way forward.
"Last week the leader of the Ulster Unionist party and myself convened a meeting of the Unionist Forum to draw together stands of Unionist thinking, both those who were elected to this house and those who were not represented. I believe this offers a vehicle for those who seriously want to discuss and address issues of concern."
Deputy First Minister Martin McGuinness said political parties must stand together.
"I think that the solution can be found in the example that was shown by all the political parties in the aftermath of the murder of two soldiers at Massereene; the murder of Stephen Carroll and the murder of Ronan Kerr," explained the Sinn Féin minister.
"What works for us is the sight of all the political parties standing together against those who believe that violence has a way forward."
He added that the disorder is challenging the political institutions, but said he does not believe those involved in violence represent the majority of unionists.
"A challenge from people who do not have a mandate and who represent nobody but themselves," Mr McGuinness continued.
"I do not believe that they speak for the vast majority of unionists within our society. These are people who are associated with the British National Party type politics.
"These are people who are clearly, to some degree, sectarian bigots."
This needs to end. Political leadership needs to be given. We all need to stand together and I absolutely believe that the PSNI need to do their job
Justice Minister David Ford, whose Alliance Party has been subjected to a number of threats and attacks during the unrest, hit out at what he called the "re-sectarianisation of Northern Ireland".
He said: "We have seen 100 police officers injured and many others injured or put in fear. We have seen the damage to inward investment, we have seen young people being given a criminal record which will damage their prospects for life.
"We have seen in fact the re-sectarianisation of Northern Ireland.
"I believe it is time we saw a united approach. We need people to wind down the language and to not build up and hype up the language which got people on to the streets in protest.
"There has to be support for the police and not the constant criticism from people who do not like operational decisions one way or the other."
Ulster Unionist leader Mike Nesbitt said the new Unionist Forum is the way forward.
"Leadership is to condemn what is wrong but also offer an alternative," he said.
"To me, that is the Unionist Forum - a political way forward where we can discuss the issues that underlie the vote on the flag."
Meanwhile the SDLP leader, Dr Alasdair McDonnell, said progress must be built on a foundation of parity of esteem for all communities.
"The whole basis of our political settlement and indeed of our future together is parity of esteem," he said.
"Peter Robinson and Mike Nesbitt are either for parity of esteem or they are not. If they are, they must make it the basis of any flags settlement.
"The protesters are denying parity of esteem. The leaders of political unionism have to make that clear. It would greatly assist in de-escalating the situation if they would make that declaration in the clearest terms possible, and make it now."
TUV leader Jim Allister said: "I abhor and without reservation condemn the repeated violence that we have seen in recent days and weeks.
"The moral authority is lacking in the House to say to people not to engage in violence because this House and its institutions and the denial of the basics of democracy -- the right to vote a party out of government or even the right to have an opposition -- are the very things that show a lack of authority in the House on the moral issues," he added.