PSNI Chief Inspector Robert Murdie was speaking after youths attacked an anti-racist demonstration on Monday.
Residents were protesting on the Lisburn Road over a spate of attacks on immigrant families living in the area.
A group of youths leaving a bar were heckled by demonstrators and retaliated with bottles and Nazi salutes.
No-one was injured in the incident.
Police were called to the scene, but the crowds dispersed peacefully and the area now appears to be quiet.
Police have said they are investigating racist incidents and criminal damage in the area over the last four days.
Chief Inspector Murdie said the number of patrols had been increased.
"It is very difficult to try to be in an area 24 hours a day to try to stop these attacks happening," he said.
"The local community are probably aware of who these individuals are."
He appealed to local people to give police names and identify those carrying out the attacks.
Protest organiser Paddy Meehan said there had been continual attacks from Wednesday.
"People are absolutely livid about what has been happening here and it has to stop," he said.
"This protest has sent a clear message that people do not want this going on in their area and that this has to stop right now."
Demonstrators had shouted "Nazis off our streets" as the youths passed and the youths gave Nazi salutes.
The Alliance Party's Anna Lo said that the trouble at the rally was a "disgrace" but that those throwing bottles were "a small minority".
"We are all here to show support for the migrant workers who have been attacked and have been hounded out from one street to another street," she said.
Earlier, two houses inhabited by a Romanian family were targeted in a racist attack.
A gang smashed windows and terrorised pregnant women and children in attacks on houses on Belgravia and Wellesley avenues.
It was claimed that the people who attacked the house were shouting Combat 18 slogans and a letter containing text from Hitler's Mein Kampf was pushed through the letterbox of one of the properties.
A number of migrant families subsequently decided to leave their homes.