On Wednesday, the Uk’s Supreme Court ruled that the PSNI was wrong to allow the protests to take place in the city.
The court found in favour of a resident who claimed the police failed in its legal duty to stop the parades.
Loyalists protested for weeks after Belfast City Council opted not to fly the union flag every day of the year.
Mr Hamilton said the Supreme Court ruling against police makes for “uncomfortable reading”, but that he accepted it.
“I apologise to the residents of Short Strand and to anyone else who was inconvenienced by this parade,” he said.
“The residents had their rights curtailed as a result of us allowing that parade to go forward, so I acknowledge that we have a job to do in some quarters in terms of regaining trust and confidence.”
Mr Hamilton said that the flag protests had presented a challenging period for the police: “There were many times when we had 80 to 120 protest sites across Northern Ireland.”
He added that he accepted and respected the Supreme Court judgement.
“It is good, actually, after four years of legal debate and a lot of scrutiny around this to have some judicial clarity,” he said.
“It is uncomfortable reading in parts for us, but it does bring some clarity to us and we will review how we handle un-notified parades in the future in light of this.”
The ruling also identified the importance of police “operational discretion”, he said.
“This judgement is not saying that every time there is an un-notified parade, the police should stop it.
“What it means is that the police have the power to stop it.
“So in some ways it’s another tactic for us dealing with this very difficult and unresolved issue in Northern Ireland.”