The "secret" documents clutched by Mr Quick were clearly on show
Police have been criticised for failing to consult specialist prosecutors properly ahead of high-profile anti-terror arrests in north-west England.
Independent reviewer of terrorism laws Lord Carlile said the police did not seek advice on whether there was enough evidence to bring criminal charges.
Twelve students were detained in raids in April but all were later freed.
Greater Manchester Police said it had consulted the Crown Prosecution Service and acted to protect public safety.
The students were arrested in simultaneous raids across Manchester, Merseyside and Lancashire as part of Operation Pathway.
The arrests were a response to what police thought was an imminent terror threat, but had to be launched a day early after Bob Quick, then head of UK counter-terrorism, was photographed holding details of the operation.
Mr Quick later resigned over the incident.
Lord Carlile told the BBC that while there was "a sound basis for carrying out arrests", there was insufficient evidence to charge the men by the time their initial period of detention was up.
By Nick Ravenscroft, BBC News
As I stood on the street corners of Manchester's Cheetham Hill, with its large Muslim population, bemused or angry people kept making the same comment to me: "It's just like Forest Gate."
They were referring to the London terror raids in 2006 on the home of two brothers in which one was accidentally shot. And no-one was ever charged.
When, two weeks after the arrests in north-west England, all the men were again released without charge, many critics of the police felt vindicated.
Well, now, a new twist. Although Lord Carlile points out the police failed to seek specialist legal advice before the raids, he does suggest there was ample justification for the arrest of at least some of the 12 men. The police will take at least some satisfaction from that.
And, crucially, there was also insufficient evidence to seek to hold them longer, he added.
"The police and the CPS were in contact, but the CPS were not asked to give specialist advice effectively until about a week after the arrests," he said.
Lord Carlile said earlier consultation might have resulted in fewer arrests being made in the first place.
But he insisted the problems had nothing to do with Mr Quick's blunder in Downing Street.
"The arrests had to be brought forward, but nevertheless there was plenty of time to obtain advice well ahead and I think that this might have resulted in a more complete operation, a better operation that would have shown terrorism law used more accurately."
He did, however, say that anyone attending any meeting "concerned with national security... should seek to avoid places where it is suspected cameras may be present".
The BBC's Nick Ravenscroft says Mr Quick's gaffe raised the profile of the operation and forced it to be carried out in daylight.
Normally raids are done before dawn, out of the public glare and when suspects are still in their beds, our correspondent says.
Assistant Chief Constable Dave Thompson of Greater Manchester Police said: "In this situation we felt we had to act to protect the public.
"We did speak to the Crown Prosecution Service ahead of arrests being made and will continue to work with them. However, none of the conversations would have changed our decision to make arrests or the number of people arrested."
Home Secretary Alan Johnson said: "As the report highlights, police need to make difficult decisions about when to make arrests based on the evidence available to them at the time, to ensure public safety.
"We will continue to work with them to review and improve operational performance and procedure where necessary."
Mr Johnson rejected Lord Carlile's suggestion that terror suspects should be allowed bail while further inquiries into their activities were carried out because of potential risks to public safety.
All but one of the men held were Pakistani nationals in the UK on student visas. One had joint UK and Pakistani citizenship.
Intelligence sources revealed some had taken photographs at destinations including a large shopping centre and a nightclub which were thought to be possible terror targets.
Greater Manchester Police said the case was still "live".