Baha and six other Iraqis were arrested when British soldiers went through a hotel in the city in September 2003 in a hunt for loyalists of Saddam Hussein, the late Iraqi president.
He died 24 hours later from wounds. A post-mortem showed he suffered 93 injuries, including a broken nose and fractured ribs.
Other witnesses have also told the inquiry that some soldiers appeared to delight in abusing the civilians, forcing one to dance like Michael Jackson and co-ordinating the screams of others in an attempt to create a form of music.
A videotape played to the inquiry showed one of the soldiers, corporal Donald Payne, screaming abuse at hooded prisoners.
Mousa gave emotional evidence to the hearing on Wednesday, weeping repeatedly as he described the affect on his family of his son's death.
He said he suffered flashbacks of the time he saw his son's gruesome injuries in a military morgue, telling the inquiry that the soldiers had breached "English dignity and honour".
Asked by Payne's lawyer Michael Topolski to accept an apology from the ex-soldier, an emotional Mousa refused. "I will not accept the apology of a criminal," he told the hearing.
"I will not accept the apology of a criminal"
father of victim
The British government ordered a rare public inquiry into the killing, asking retired Court of Appeal judge William Gage to investigate the circumstances of Mousa's death and to make recommendations for possible changes to military detention techniques.
Mousa told the hearing that he had accused a British soldier of stealing bank notes during the hotel raid and that his son was targeted by troops in revenge.
Mousa's death has already led to the conviction of Payne as Britain's first war criminal in Iraq.
He was dismissed by the army and sentenced to a year in prison for inhuman treatment in 2007.
Britain's defence ministry has previously apologised for the mistreatment of Mousa and nine other Iraqi men, awarding them a shared $4.9 million settlement.
Mousa said that on the night of the hotel raid he arrived to collect his son from work, only to see military vehicles surrounding the building and staff lying face down on the ground, including Baha.
He said he saw a British soldier stuff bank notes from a hotel safe into his pocket and passed on his concerns to the man's superior , whom he identified only as "lieutenant Mike".
Mousa said he pointed his son out to the soldiers, hoping troops would release him in return for bringing the alleged theft to their attention.
"I think they knew the one I was pointing to was my son, therefore they wanted revenge against me on him," Mousa said.
Outside the hearing, Mousa said he believed "without the slightest doubt" that his son was attacked in retribution.
Lawyers representing the Mousa family have urged the inquiry to consider whether military officials sanctioned soldiers in Iraq to use interrogation techniques banned by Britain in 1972, amid controversy over the use of the methods in Northern Ireland.
They told the inquiry earlier this week that soldiers used so-called "conditioning techniques", including stress positions, hooding, sleep deprivation, food deprivation and white noise.