The family of Kingsley Burrell, who died in hospital in 2011 days after being forcibly detained by the police, have renewed their calls for a public inquiry after one of the officers involved was sacked for lying about the events leading to the death, as well as failing in his duty of care.

PC Paul Adey of West Midlands police was found to have committed gross misconduct by an independent panel on Tuesday, though two other officers were cleared.

That led Burrell’s relatives, who have led a years-long campaign for a full inquiry, to demand action from the government. A spokesman said: “This is not the end of the road for our quest for justice, as it is now our intention to renew our calls for a public inquiry into this.”

Burrell’s family said the day of his death was “etched on our hearts forever”, remembering him as a “son, father, brother, uncle, cousin, friend and human being”.

They called for all of the agencies involved in the 29-year-old student’s detention and care to be “held to account for their collective failings, not just to Kingsley and his family but also the people of the West Midlands, who expect a substantially better quality of service to us all, irrespective, of our race, colour, gender, age or ability”.

Burrell died in Birmingham, days after being detained under the Mental Health Act. He had called police on 27 March saying he was being threatened with a gun but officers became concerned when no evidence of a firearm was found.

His inquest heard that he had been left handcuffed for hours in hospital while awaiting assessment and, after struggling with medical staff and police officers, was left face-down in a secure room with a blanket over his head.

When a check was carried out, Burrell was found to have suffered a cardiac arrest. He never regained consciousness and died on 31 March.

After six weeks of evidence, an inquest jury found that prolonged restraint and a failure to provide basic medical attention had “more than minimally contributed to his death”. They concluded he had died as a result of neglect, but Burrell’s relatives were disappointed that jurors had not been able to consider a verdict of unlawful killing.

Adey, one of the response officers involved in the incident, told Burrell’s inquest he did not remember if Burrell’s head had been covered with the blanket but was found on Tuesday to have lied about his recollection of events. The allegations against two other officers who had said the same were found to be not proven, leading Burrell’s family to criticise the panel.

In October last year, the three officers were found not guilty of perjury by a jury at Birmingham crown court after being accused of misleading the 2015 inquest into Burrell’s death.

Louisa Rolfe, the deputy chief constable of West Midlands police, said: “We do not underestimate how upsetting this investigation has been for Kingsley’s family and friends.

“Kingsley was in mental health crisis and deserved to be looked after in a place of safety. His family, quite rightly, should have expected him to be cared for and protected, but they were all sadly let down.”

She added that all of the agencies involved in Burrell’s care “had a responsibility to ensure his safety and we all failed him to different extents. I am very sorry for our part in this failing and the hurt this caused.”

• This article was amended on 19 December 2018. An earlier version stated that Burrell died in police custody. This has been corrected.