The former head of the British army has denied there was a cover-up after soldiers shot dead 10 people in the so-called Ballymurphy massacre, one of the most controversial episodes of the Troubles in Northern Ireland.

Gen Sir Mike Jackson told a coroner’s inquest in Belfast on Thursday that he had no explanation for the apparent lack of a serious investigation in the aftermath of the killings but said the military had nothing to hide. “We don’t do conspiracies,” he said.

He gave his testimony in a courtroom packed with relatives of those who were killed in Ballymurphy, a neighbourhood in west Belfast, in a tumultuous 36-hour period in August 1971. The dead included Joan Connolly, a mother of eight who was shot in the face, and Fr Hugh Mullan, a Catholic priest shot while giving last rites to a wounded man.

No guns were recovered from Ballymuphy. Relatives say the dead were innocent civilians who were later smeared as terrorists to justify a rampage by paratroopers.

Jackson was at that time a captain in the parachute regiment and was deployed to quell disturbances in Ballymurphy. He later rose up the ranks and became chief of the general staff before retiring in 2006.

In his testimony the 75-year-old reiterated the official version of events: that troops waged a fierce gun battle with the IRA in Ballymurphy. He said he heard the “distinctive thumping noise” of a Thompson submachine gun, a weapon of choice for the “enemy”. “I have absolutely no doubt that the IRA were firing on soldiers and soldiers were firing on the IRA.”

Jackson rejected a suggestion that the military sought to hush up a brutal effort to intimidate the local population. “It is a preposterous accusation to make which would require a huge number of people to be part of,” he said. “It simply does not add up.”

He said it was hard to describe the chaos and conceded there might have been a “breakdown” in military procedures to record use of force: “It may be that the whole system was overwhelmed by the mayhem of that week, I don’t know.”

Jackson’s appearance in the Laganside courtroom, separated by three miles and almost half a century from events in Ballymurphy, drew a rapt audience in the public gallery.

“This is a big day for us,” said Maura McGee, 57. She was nine when she lost her mother, Joan Connolly. “They left Mummy out in the field for hours. She bled to death,” she said.

Gerard Teggart, 61, was 13 when his father Daniel Teggart was killed. He said he had attended each day of the inquest, which began last November. “I hope this general has the decency to tell the truth,” he said.

Other former soldiers have in recent weeks given conflicting testimony. Some have repeated the version in which there was a firefight that killed IRA members and caught civilians in crossfire.

In contrast, a former corporal, identified by the code M597, said some paratroopers were “out of control” and “psychopaths” who considered anything that moved a legitimate target.

Violent protests flared across Northern Ireland on 9 August 1971 when troops started rounding up republicans who were to be interned without trial. Hundreds of homes were destroyed and thousands fled across the border.

A 2014 Guardian article and interactive map that reconstructed events in Ballymurphy found that residents erected barricades and clashed with Protestants in neighbouring Springmartin. Youths threw stones and petrol bombs. A small number of shots appeared to have been fired.

Some residents were fleeing when soldiers started shooting into the Catholic area, firing so many rounds they ran low on ammunition. Soldiers “were on a high”, according to one paratrooper’s memoir.

There were no camera crews were around during the killings, leaving the events largely overlooked by the outside world, unlike Bloody Sunday in Derry, which unfolded months later.

Jackson told the inquest he was probably the unnamed captain who referred to Ballymurphy’s first two fatalities as “gunmen” in an interview with the Belfast Telegraph. He heard but did not see shooting and likely was repeating information from comrades, he said, adding: “In retrospect, of course I should have said ‘alleged’.”

He offered sympathies to the relatives of the 10 dead. “It’s a tragedy which is hugely regrettable, but I would also say that anybody who loses their lives as a result of violent conflict is also a tragedy. I too have lost friends, so be it.”