Speaking to UTV on Thursday, the First Minister said that the unionist community "had every right to be angry" over the issue.
Mr Robinson's comments came after the Orange Order earlier accused the Parades Commission of creating crisis and called for its members and supporters to engage in peaceful demonstrations.
"What we've said today is that the Twelfth parade will not be over till all the brethren, bandsmen and supporters are home," Orange Order chaplain Rev Mervyn Gibson told UTV.
Friday morning's parade is set to take place in the Ardoyne area with no music or drumbeats and with only 100 supporters allowed to accompany the lodges and bands.
On their evening return parade, Orangemen and bandsmen will be stopped at the junction of Woodvale Road and Woodvale Parade.
Three Lodges have been banned from going along the Crumlin Road. We're saying that, until they get home, the rest of the Twelfth day isn't over for everyone else.
Rev Mervyn Gibson, Orange Order
Reacting, Mr Robinson said: "Here is the dilemma that the Parades Commission have created - are people not allowed to express their anger at these matters?
"That was the reason that my colleagues and I put down a motion for the recall of the assembly, so there can be an outlet for the anger and also to give an opportunity to those from the nationalist republican tradition to put out very clearly what is their intention when they talk about a shared society."
The DUP leader added that he supported the Orange Order in their call for protests to be carried out in a "peaceful manner".
"There will be further protests," Rev Gibson said.
"We're not going into detail of what those are. But certainly, anything that takes place, we want it to be peaceful.
"It's not inevitable that there'll be violence and we've protested before where there's been no violence and we hope that's the case again."
There is a lot of anger within the unionist community and it is justified and it justifies protest.
First Minister Peter Robinson
The nationalist Greater Ardoyne Residents' Collective (GARC) has already called off a protest march in the area during the afternoon, following the Parades Commission's ruling.
But the group still plans to stage a morning protest.
Another group, Crumlin Ardoyne Residents' Association (CARA) have also decided to call off a protest on Friday morning.
A total of 4,000 officers will be involved in a major security operation across Northern Ireland on Friday.
Following a meeting with PSNI Chief Constable Matt Baggott on policing preparations, NI Secretary of State Theresa Villiers expressed concern about protests being held on the Twelfth of July.
"Those who are calling people on to the streets at a time of heightened tension must be aware of the possible consequences of their actions and the potential risks to public safety that could result," she said.
"I fully appreciate how strongly people across the community feel about parading. But it's hugely important that they continue talking to each other and that they abide by the rule of law."
Ms Villiers added: "I know there is anger in the loyalist community about the Parades Commission's determination. But the reality is that the Commission is the lawfully constituted authority and its determinations have the full force of law."
People have a responsibility not to encourage, incite or say anything that makes that less likely. There are criminal responsibilities not to incite anything that makes them criminally culpable.
Assistant Chief Constable Will Kerr
PSNI Assistant Chief Constable Will Kerr also appealed for responsible leadership and behaviour.
"If people exercise those two things, we are confident people can go home safely," he said.
"Irrespective of what the determination had been, and we understand there is frustration and anger in one community, we will uphold that determination tomorrow.
"But we want to uphold it in a way that there is no violent confrontation and that nobody gets hurt. People have a choice to make tomorrow."
Sinn Féin MLA for North Belfast Gerry Kelly said that, while he respects everyone's right to protest, he would urge the leadership of the Orange Order to carefully reflect upon the decisions they make in the coming hours and days.
"There is an opportunity for the Orange Order to step forward and make a decisive contribution to the peace process," he said.
"They can, by their actions, decide whether the Twelfth will be remembered for the Orangefest type event they claim to want - or by protests and tensions on the streets.
"I would argue that the vast majority of people would want them to choose the former. The Twelfth should be celebrated in ways which are not threatening or triumphalist to their nationalist neighbours."
All of us have a responsibility to ensure a peaceful summer. The sort of language used today by the Orange Order in my opinion serves only to heighten tensions in an already tense situation.
Gerry Kelly, Sinn Féin MLA
The Orange Order's announcement also came as DUP North Belfast MP Nigel Dodds continued to call for Theresa Villiers to intervene - a day after he was expelled from the House of Commons.
The DUP deputy leader refused to retract a claim that the Sectretary of State had been "deliberately deceptive" - which goes against parliamentary rules, whereby one MP cannot accuse another of lying.
Speaker John Bercow asked him three times to take back the comment, before suspending him from the House for the rest of the day.
"I have no apology to make whatsoever," Mr Dodds told UTV.
"I remain absolutely adamant that the Secretary of State has got to do more - she can't sit back, she has to take responsibility. The Parades Commission answers to her, not the local Assembly."
Ms Villiers said in the House of Commons that she is powerless to act until the PSNI Chief Constable Matt Baggott makes an application for her to intervene.