Four cars and the living room window of a home were damaged in the Ringford Park area after a crowd of up to 100 nationalist youths went on the rampage on Friday night.
They ran along Blacks Road after they left a house party which was reported as "out of control".
The DUP claimed there were further attacks on Monday evening. They said stones were thrown from the Stewartstown Road into Carnanmore Park and a car windscreen was broken, shortly before 7pm.
"It's very disappointing that there has been a further attack on Suffolk this evening," local DUP councillor Brian Kingston told UTV.
"So soon after that meeting, which went very well, more innocent residents have been attacked and I understand the police have been out."
Earlier, DUP and Sinn Féin representatives described the attacks as "sectarian".
"There is a lot effort goes on between the two communities. There is contact, but unfortunately sectarian attacks do occur from time to time," Mr Kingston explained. "This particular incident on Friday night just stands out in particular because of the scale of the attack.
"It seems that what they did was gatecrash a party in the Brooke Drive area and caused damage there. Then unfortunately they decided to launch what can only be described as a deliberate sectarian attack against Suffolk estate.
Relations in that area are very good and we must ensure that Friday night's incidents don't harm those relations.
Gerry McConville, Falls community representative
Speaking after a meeting with police at Woodburn Station, he added: "The police said that they have four officers dedicated specifically to the investigation into the events of Friday night.
"They currently have diverted their interface police land rovers, three land rovers, dedicated to the Suffolk area to provide reassurance and protection for the area."
Also at the meeting was Matt Garrett, a local Sinn Féin councillor, who said the attacks were not representative of those living in the area.
"Clearly the people who came into the area on Friday night did so with the intent to cause mayhem and havoc throughout this entire community," he said.
"We want to lend our support to the people of Suffolk estate," he added. "This attack was wrong, it shouldn't have happened and they whole-heartedly have our support."
Gerry McConville, from the Falls Community Council, described Friday night's events as "totally wrong".
"It was a pure sectarian attack on the people of that area and must be condemned by all right-thinking people," he said.
"We've been working quite hard along that interface and other interfaces across Belfast to make sure that people are living free from sectarian crime.
"I have been speaking to residents from a small Catholic estate beside Suffolk, who initially were on the scene and saw this crowd coming up and tried very hard to stop the crowd going up the Blacks Road, unfortunately they were just overwhelmed with sheer numbers."
Mr McConville explained that representatives from both communities also met on Saturday, which he said was very constructive.
He added during Monday's meeting that he would inquire whether nationalist representatives should visit the area to see the damage.
"We must make sure that the people who carried out that attack do not win and do not get their way and that these attacks stop," he said.
"I think it's very very important that the ordinary residents of Suffolk know how much we abhor the attacks."