Det Supt Eamonn Corrigan described his murder “as a calculated, planned, ruthless execution”.
“At one point, both gunmen stood over Sean, shooting him, as he collapsed to the floor,” the officer said.
Mr Corrigan added that the attack took place “in broad daylight” in front of several witnesses and the victim was “singled out” as he sat enjoying a drink.
Murdered ‘in under a minute’
Footage of the suspects outside the venue has been posted on the Police Service of Northern Ireland’s YouTube account.
It shows two masked men in hooded tops entering the grounds of the social club and leaving on foot in the direction of Gweedore Gardens.
“The gunmen arrived, carried out the murder and left the club in under a minute. They were inside the premises for approximately 21 seconds,” Mr Corrigan said.
“This cold-blooded act has taken a man’s life. It has left a family bereft, and many others in the local community shocked.
“This barbaric act has no place in any society.”
Mr Fox was a married father of two who was a regular customer of the social club.
At a press conference on Tuesday, the police confirmed the killers fired 20 bullets inside the busy function room and “multiple strike marks” have been identified in the premises.
“Anyone in that room or indeed nearby, could have been killed or seriously injured on Sunday,” Mr Corrigan added.
Mr Corrigan was asked if the PSNI believed there was a connection between the friends’ murders.
The officer replied: “We are looking at all previous shootings and seeing if there are any links.”
His colleague Ch Supt Darrin Jones said the PSNI’s thoughts were first and foremost with the victim’s family.
“There’s been some speculation about the motive for Sean’s murder,” he told reporters.
“Only those who were involved know how they could attempt to justify the brutal murder of a family man. I want to be clear, there can be no justification or acceptable explanation for the murder of Sean Fox.”
Mr Jones added that the PSNI recognised that the shooting was “an attack on the fabric of the local community” and they have “increased resources across west Belfast”.
£20,000 reward
Appealing for help from the public, Mr Corrigan said the killers had concealed their identities and had left “little forensic opportunity” in what would be a “challenging” investigation.
Giving a description of the suspects, he said one of the men was wearing “a blue hooded-top, a peaked baseball cap, dark face covering, two-toned gloves (pale on top and dark on the bottom), dark-coloured bottoms and dark shoes/trainers”.
He added that the second suspect was wearing “a distinctive light (possibly grey) hooded-top with three red lines down each arm, a peaked baseball cap, a light-green face covering, two-toned gloves (pale on top and dark on the bottom), dark-coloured bottoms and dark shoes/trainers”.
A reward of £20,000 has been offered for anonymous information which leads to the conviction of Mr Fox’s killers.
It has been offered by the Crimestoppers charity, which is independent of the police.