Children picked up a bomb outside Woodbourne Police Station on the Anderstown Road in Suffolk on Monday evening.
It was one of two devices thrown at the back of the station on Monday night, one of which exploded. There are no reports of any injuries.
Police said children picked up an unexploded device and brought it to the front of the station.
The explosion happened about 22.30pm and the second bomb was found at about 23.00pm.
It was made safe by the Army.
Chief Superintendent George Clarke said the attack was an attempt to kill and maim police officers.
“In doing so they were absolutely reckless as to the consequences for local people and as to the consequences for those children,” he said.
“These are not commercially manufactured, stable items, these are extremely volatile, very, very dangerous, utterly lethal devices which could function [explode] at any time.”
Chief Supt Clarke said he believed dissident republicans were responsible and said they were people who had not moved forward and had not listened to the condemnation from all sides of the community.
“I can’t see the logic in throwing bombs at the back of a police station and leaving an unexploded one for children to pick up,” he said.
Councillor Brian Kingston said a number of people were moved from their homes in Lenadoon and the Suffolk estate due to the incident.
He said it had all the hallmarks of a dissident republican attack and was a “cowardly attempt to kill police officers”.