He said the main parties have been "silent" in rejecting the violence which followed the removal of the Union flag at City Hall last year, and since the Twelfth.
Speaking at a republican commemoration in west Belfast on Sunday, Mr Adams also hit out at "illegal marches" and the "provocative actions of the Orange Order in Belfast".
The Louth TD said: "The silence of unionist leaders to all of this has been deafening. No condemnation - no rejection of the violence and the threats.
"These are the same parties that used to lecture republicans about the 'rule of law' and who demanded that before they would reach agreements Sinn Féin had to sign up to policing.
These are the 'law and order' politicians! Such hypocrisy - such double standards!
"The lack of real leadership by unionist leaders has had a negative effect on public opinion and confidence in the power sharing institutions is being undermined."
This weekend the Orange Order said it intends to "upscale" its protests over a Parades Commission ruling preventing three lodges from marching past the Ardoyne shop fronts.
William Mawhinney made the remarks as around 500 loyalists gathered for a peaceful protest on Saturday, following two failed applications to complete the 12 July route.
He said: "When the time is right we will probably upscale our protests and that's just what we intend to do, upscale them right up until civil disobedience if that's what it takes."
Nigel Dodds of the DUP, who was at the demonstration alongside a number of party colleagues, told UTV any protests should be "peaceful" and "within the law".
He continued: "I think people are angry and frustrated at the denial of human rights at the bizarre and irrational decision of the Parades Commission and people will decide in the fullness of time how the protest should be maintained."
Earlier this year violence erupted as loyalists clashed with police who enforced a Parades Commission ban on Orangemen walking part of the Crumlin Road on the Twelfth.
As was said from the platform, the protests must be within the law, peaceful, and that is the way to move forward.
Bands had hoped to march the rest of the route at 9am on Saturday morning, but this was rejected by the commission. A further request to march in the afternoon was also rejected.
The application for the morning march was put forward after the Orange Order announced negotiations with residents, as part of what it calls the Twaddell Initiative, will only start after Orangemen complete their return parade past the Ardoyne shops.
The Parades Commission said that it was disappointed the lodges had not commenced dialogue with involved parties. It reaffirmed its call for "sincere and sustained" dialogue as the best route map to resolve parading issues at Ardoyne.
Alban Maginness of the SDLP said he was let down by Mr Mawhinney's remarks.
He told UTV: "I'm very, very disappointed. What I have said to the Orange Order and others who are demonstrating in Ardoyne is what they should do is suspend their operations during the Haass process and that will give everyone breathing space to examine these issues."
American diplomat Richard Haass will return to Northern Ireland later this month to continue all-party talks aimed at resolving issues such as flags, parades and the past.
Responding to the comments made in Mr Adams' speech, UUP councillor Mark Cosgrove said his party has "always had no difficulty in saying that violence is wrong".
He continued: "Given Gerry Adams' huge and growing credibility gap, I am not surprised by his latest factually incorrect comments. It is clear that Gerry Adams obviously hasn't been back in this part of the United Kingdom lately.
"We will always promote and defend the right of aggrieved citizens to peaceful protests as these are basic rights in any democratic society. Unlike Gerry Adams, the Ulster Unionist Party has always tried to do what`s right for Northern Ireland and its citizens."