Anderton issued the plea this afternoon as he confirmed his resignation from his post at Murrayfield in the wake of ally Mackay being forced out by the SRU's general committee.
Mackay had proposed a radical re-structuring of the game in Scotland and his plans are due to be voted on by the clubs on January 30 at a special general meeting.
Anderton is furious with the general committee's move to pre-empt the sgm by issuing a vote of no confidence in Mackay, describing his own resignation as "probably the saddest" decision he has made in his life.
With a power vacuum at the top of Scottish rugby and with talk of a players revolt, Anderton sees the clubs as key to ending the crisis prompted by disagreement between the general committee - set up to represent the game's grassroots - and the professional administrators on the executive board over the future of the Scottish game.
In their place, he wants a single decision-making body.
He said: "I'm here to ask the clubs to rise up and take a decision and act to stop this folly once and for all.
"The clubs must put forward a motion, an amendment to the sgm for the immediate re-instatement of David MacKay, and have a change of governance.
"We need a single governing body that is responsible for decision-making power, with the clubs the ultimate decision-maker with the opportunity to remove or hire the people that make the decisions on their behalf.
"If they do not take this action they are effectively endorsing the decision to remove the chairman of the executive board and they will have to bear that on their conscience."
Anderton was candid in pointing the finger of blame for the crisis firmly at the general committee's door when he met with journalists in a hotel in the shadows of Murrayfield.
Mackay, who has been credited with slashing the SRU's annual losses by over £7million, was keen to reduce the general committee's power as part of the restructuring.
Anderton added: "I was very excited about the way forward for Scottish rugby and we didn't expect everyone to buy into every single part of the plan.
"We believe we had a great opportunity to fundamentally change the game at the top end and at the grass roots.
"I'm not prepared to continue to work in the new changed environment because, make no mistake, the general committee are running Scottish rugby and I have seen that at first hand this week.
"Everyone knows what this is all about, it's governance, who runs the game?
"There is information going out that the executive are trying to de-power the clubs, what absolute nonsense!
"We were trying to ensure the clubs had the absolute responsibility and accountability and a direct involvement in the running of the game.
"How many clubs wanted to get rid of David Mackay and are they happy with the decision?"
While four members of the executive board plus Anderton have resigned or been forced out this week - non-executive directors Fraser Livingston, Andrew Flanagan and Eric Hagman left in the wake of Mackay's departure yesterday - the row claimed its first casualty on the general committee.
Iain Brown, the committee's schools representative, stepped down today.