On Wednesday, the 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.
On Thursday, 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."

It includes the Buckskin area of Basingstoke, where more than 80 homes were evacuated in February 2014 after groundwater flooding.
Hampshire County Council can now access a Â£2.1m fund a year earlier than originally expected from 2016-17.
Schemes for Romsey and Winchester can now access funding immediately rather than having to wait until 2020.
Many residents in Buckskin were unable to return to their homes until the following winter after more than 77 million litres of water had to be pumped out.
An independent report recommended a review of the area's drainage system and the "setting up [of] a threshold at which point actions should be taken".
Hampshire County Council has already started the first phase of a feasibility study to mitigate flooding. The funding is subject to the approval of a business case.
Cleansing and repairs to the existing infrastructure in Buckskin has already started while an electricity substation has been moved.

Lines in and out of Cardiff Central were closed early on Thursday morning after Network Rail's re-signalling work went on longer than planned.
They reopened at 08:15 GMT but disruption has continued to cause services to be cancelled or delayed.
Arriva Trains Wales hoped services would run on time by late evening.
Sophie Holley was waiting to catch a train home to Rhoose in Vale of Glamorgan when it was cancelled, so had to arrange a lift instead.
She said: "It's a bit of an issue, we've got to wait around in the cold now with a little one - it's a bit annoying."
It added there was still severe disruption to Valley line services, but it said trains to Penarth, Coryton and Cardiff Bay would be reinstated throughout the day.
Meanwhile, Maesteg services will start and terminate at Bridgend and a shuttle bus will run between Bridgend to Cardiff, calling at Pencoed, Llanharen and Pontyclun.
Replacement buses have been put on between Cardiff and Newport and tickets for Cardiff rail services will be accepted by Cardiff Bus.
Passengers took to Twitter to vent their anger at the delays.
Dan Walsh wrote: "Sheer madness at Cardiff Central today: not good enough @ArrivaTW @GWRHelp @nationalrailenq."
Rich Griff tweeted: "@GWRHelp been sat at a standstill outside Cardiff Central for over an hour. Anyone planned on travelling to Cardiff today. Don't bother."
Arriva Trains Wales said: "We apologise for this disruption and would advise all passengers to check before they travel at www.arrivatrains.wales/check for the latest information on disruption to services and assure them that we are doing all we can to get trains back on schedule as quickly and safely as possible."
PSNI Chief Constable George Hamilton has apologised to residents in the Short Strand area of Belfast over the handling of the union flag protests.
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Central government funding has been brought forward for a number of flood defence schemes across Hampshire.
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Rail disruption continues across south Wales following earlier cancellations between Cardiff to Newport after engineering works overran.