Cameron said it had been the "wrong decision" to make the News of the World editor his media chief in 2007 though denied ignoring warnings about Coulson's activities at the tabloid, which Rupert Murdoch shut down in disgrace in July 2011.
The eight-month phone-hacking trial came to an end as jurors were sent home without reaching a verdict on two further charges that Coulson faced relating to alleged payments to police officers.
Judge John Saunders said he had rejected a request by Coulson's defence lawyers to halt proceedings on the basis that jurors might be influenced by the premier's views.
"That does not mean that I am not concerned about what has happened in this case," Saunders added.
More From This Section
Cameron hired Coulson just months after he resigned as News of the World editor in 2007, soon after the jailing of the paper's royal editor and a private investigator for hacking.
"I always said that if (Coulson's) assurances turned out to be wrong I would apologise fully and frankly to this House of Commons and I do so today from this despatch box. This was the wrong decision," Cameron told the House of Commons.
Opposition Labour leader Ed Miliband said the charge against Cameron was "not one of ignorance but one of wilful negligence".
The high-profile trial centred on the News of the World's efforts to hack the phones of Britain's royal family, politicians, celebrities and victims of crime.