In his final submission to day 431 of the Saville Inquiry, Lord Gifford QC said the inquiry needed to pronounce in its report on the responsibility of British political leaders, including Mr Heath, for "the disaster of Bloody Sunday".
The then Prime Minister had authorised tough action knowing there was a risk of bloodshed on a potentially large scale, he said.
It was a very serious part of the inquiry's remit to pin down the extent of responsibility among Mr Heath and his ministers, he said.
"It is serious for the reputation of men who have held the highest office of state.
"It is important for the families also that you should pronounce up to what level, military and political, you hold people responsible for the acts of the soldiers on Bloody Sunday."
Prior to Bloody Sunday on January 30, 1972, a choice had been made, initially it seemed at a military level, to allow a measure of tolerance for unlawful marches, he said.
But he said: "By the end of January the choice was made to enforce the law with rigour. In the making of that choice, the Prime Minister played a decisive role."
Mr Heath "did not urge restraint" he said. "He felt no need because he had made a choice that the law should be observed, if necessary at the cost of damage to the marchers at the hands of the army."
"We say it was plainly obvious that if you authorise the army to be resolute in confronting a march of 8,000 to 12,000 citizens, confronting them with 20 companies of troops, you are risking bloodshed on a potentially large scale," he added.
Earlier, the lawyer branded soldiers who opened fire on Bloody Sunday as a "death squad". Lord Gifford is representing the family of James Wray, 22, who was shot dead in the Bogside by paratroopers. He said Mr Wray was "murdered by a group of soldiers who called themselves a brick but that we have called a death squad".
Mr Wray was shot once in the back as he fled and once more at close range as he lay on the ground, said Lord Gifford.
He and others fired on were shot "for no other reason than that they were easy targets", he told the inquiry in the Derry Guildhall.
Each of the four soldiers in the group had offered a pretext for opening fire which had been "contradictory and manifestly false", he added.
The lawyer said that if it had been a case of a "squad of underworld hit men shooting members of a rival gang, there would have been no hesitation in a prosecuting authority in charging every member of the squad with the murder of every victim who died."
He questioned when the "common purpose" had been formed to open fire that day and said there had been a sense of anger among the paratroopers sent into the city for the march that the youths of Derry had previously been treated with "undue restraint" by the resident troops.
Lord Gifford said there was a "sense of resolve that the exercise on Bloody Sunday was an opportunity to teach them a lesson".
The shot which killed Mr Wray had not been fired out of a sense of danger but deliberately to "get a kill", he added.
He referred to the words of one of the soldiers during the shooting of Bloody Sunday 'I have got another one' and said it was "the triumphant report of a team member who has done what the team expected of him".