Mr Adams condemned violence orchestrated by dissident republicans in north Belfast where around 20 police officers were injured and where at the height of the disturbances a live round was fired at security forces.
In one of the worst nights of violence in recent years there were also clashes with police in areas including Armagh, Londonderry and the village of Rasharkin, Co Antrim, as the Orange Order marked the height of its marching season.
Mr Adams said the vast majority of 2,000 to 3,000 loyal order parades held throughout each year passed off peacefully and he said talks should take place between his party and the Orange Order to resolve problems that remained at a small number of locations.
The Sinn Fein leader said: "Let's get all of this in proportion, there were about 100 parades yesterday, there are 3,000 Orange parades annually, there are about six contentious parades and last night's disturbances, whether in Ardoyne or in Armagh or in Rasharkin, involved a very, very small minority of people... being exploited by some of these so-called dissident groups.
"But let's look at the big picture in terms of what it used to be like and what it's now like.
"What happened last night is wrong. It's reprehensible. And all of us who are leaders, and I include the Orange leadership, have a duty to look at how these disturbances occur.
"There was a very peaceful demonstration organised both on the outward and the inward legs of last night's parade, so there is no support in Ardoyne for this parade going down this route - the only people who want to go that way are the Orange.
"And I would appeal to them in terms of these six or seven contested parades to talk, or not to go in. Why not have their Orangefest celebrations without... playing into the hands of these small groups."
Mr Adams said Orange Order leaders should remove their refusal to hold talks with elected Sinn Fein politicians.
"My biggest frustration is that thus far the Orange Order has contributed nothing to the peace process.
"The Orange Order still refuses to talk to Sinn Fein... even though Martin McGuinness is the deputy First Minister, even though there are a number of Sinn Fein ministers, even though unlike them we have a mandate which we renew at every election.
"They talk about being a Christian organisation, about neighbourliness, and I don't dissent from any of that and I don't say any of this to undermine the good decent people who were involved in the Orange, but why on earth can't they come forward and meet us."
Mr Adams told the BBC that he had met Orange Order members in Portadown who are linked to the long-running Drumcree parades dispute, but he said the leadership of the Order still refused to deal with his party.
Democratic Unionist Party (DUP) Culture Minister, Nelson McCausland, said marchers spoke to residents in the Ardoyne area and community leaders in a local parades forum.
He also said the Order had made strides in rebranding the July 12 parades as Orangefest as part of efforts to create a more family friendly and inclusive atmosphere.
In a break with tradition, city centre shops opened in Belfast for a period yesterday, as normal routines were maintained while accommodating parades in the morning and early evening.
Nationalists have complained over the route taken by some marches through areas that are predominantly Catholic, or in the case of Ardoyne, past a sectarian interface. They have criticised aspects of the Orange Order and wider loyalist element to the marching season, including the scale of some loyalist bonfires on July 11 and the presence of anti-Catholic slogans.
But Mr McCausland said the major issue was the scale and ferocity of last night's dissident violence.
"If someone makes sectarian comments no matter who it is or where, I don't condone that in any way," he said.
"I think the focus should certainly be not only on some comments here or there and you can find comments in every community across Northern Ireland, it is far from a perfect society.
"What we do have is a situation this morning is where we are looking at a legacy last night of guns or guns being used, vehicles being burned and people being attacked, attacks on policemen and those are things that are appalling and indefensible."
Dissidents republicans were blamed for the confrontations in Ardoyne where nationalists attacked police lines after crowds gathered ahead of the return parade by Orangemen from their July 12 demonstrations.
Petrol bombs, fireworks, stones and bottles were hurled at police, who used water cannons and fired 18 baton rounds to fend off attackers.
Two vans were hijacked and pushed at police lines.
In Londonderry there were disturbances that saw 11 petrol bombs thrown and one police officer injured.
There was also trouble in Rasharkin, County Antrim and Armagh city, while security forces also had to deal with hoax bomb alerts in Strabane, Co Tyrone, and in Lurgan, Co Armagh.
Police assistant chief constable Alistair Finlay said: "They displayed the worst possible face of Northern Ireland - a face of bigotry, sectarianism and intolerance that is not representative of the vast majority of people who have moved on and embraced a peaceful future."
In Rasharkin, officers sustained minor injuries when they were struck by stones and bricks by youths in the village.
Petrol bombs were hurled. One man was arrested.
There were disturbances during the return leg of the Twelfth parade in Londonderry and violence in the Butcher's Gate area where one policeman sustained an injury.
Police came under attack with petrol bombs and paint during disturbances in Armagh following a security alert at Friary Road in which a minor explosion occurred.
Four people have been arrested for public order offences following a number of minor disturbances.
At least two cars were also stolen and set alight on Friary Road.
* This article is from The Belfast Telegraph
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