It exploded at around 10.30pm after being left close to the entrance of the Belfast City Cemetery
Police confirmed on Saturday morning that four officers and several members of the public were caught up in the explosion.
A PSNI statement said that when the device detonated, it caused damage to the police vehicle and a cemetery wall.
A Filipino family of four - including children aged 11, 13 and 16 - were caught up in the explosion.
Their car was badly damaged and they were treated for shock.
A young pregnant woman was driving past with her 3-year-old nephew when the attack happened.
Paula Morrison was taken to hospital afterwards as a precaution.
"I just froze," she said, adding that both she and her little nephew were left shook up by the blast.
"We told him it was a firework, but when he went to his daddy's [house], he said 'No daddy, it was a big bomb."
Ms Morrison told UTV that she couldn't help but think about what could have happened the child had her car been struck with debris.
She said that she is now afraid to drive on the Falls Road incase the perpetrators strike again.
Dissident republicans are being blamed. The Falls Road re-opened on Saturday afternoon after police finished follow-up searches.
Detectives are appealing for anyone who noticed any suspicious activity in the area of the City Cemetery in recent days or anyone who has any information to contact them.
Superintendent Barbara Gray said: "This was not only a deliberate attempt to kill police officers but was an attack on the community of West Belfast, and it is only through good fortune that no-one, either police or civilian was seriously injured or killed last night.
"As with all incidents a review of the police response will be carried out to ensure that we do everything possible to provide the highest quality response to the communities of North and West Belfast."
When will those who tried to kill police officers on the Falls Road get the message? They are not supported and their actions are futile.
Justice Minister David Ford
"It is fortunate there were no injuries sustained by police or the family whose car was damaged. I send my best wishes to the police officers and the family affected.
"The people behind this attack clearly planned it but I wonder what their plan was had members of the public been injured or killed? The Falls Road is a main route with a constant flow of traffic and pedestrians and it was totally irresponsible to carry out this attack on the local community."
Meanwhile, the chairman of Northern Ireland's Police Federation is calling for a PSNI security review across the region following the blast.
Terry Spence, Police Federation chairman, described the attack as "both reckless and futile."
After discussions conducted between the federation and some of the PSNI senior command team, Mr Spence told UTV that there must be a fundamental review of security "in light of the worrying escalation in dissident republican violence."
"We've asked for that review and we've been told by the PSNI that there will be a review right across the province, but in particular north and west Belfast.
"The officers were fortunate to escape unhurt in what was a clear attempt to murder and maim. Those responsible have absolutely no regard or respect for life. It was a reckless, cowardly and futile action by individuals who have nothing to offer.
"My members will continue undeterred to offer a professional service to the community," Mr Spence continued.
"These terrorists will not succeed in their goal and I would appeal to anyone with information to get in touch with the PSNI so that these mindless people are brought to justice.
"Police officers and the public must remain vigilant as it is the obvious intention of desperate dissident republicans to attract a headline in the run-up to St Patrick's Day."
On Friday morning, also in west Belfast, the discovery of an under-car booby trap bomb sparked a security alert.
The viable explosive device was discovered by a passing police patrol in the Blacks Road area near the junction with Arlington Drive just before 8am on Friday.
Homes were evacuated in the area while the device was made safe. Dissident republicans were blamed for the device.
Mr Spence said that the two incidents, which happened in the space of 24 hours, could have resulted in death or injury to police officers or civilians.