Keith Bristow said expecting all the estimated 50,000 people in the UK who have accessed abuse images to be brought to justice was "not realistic".
He said police would have to focus on those who posed most risk.
Labour called it "disgraceful", adding that the NCA was not fit for dealing with the problem. The Home Office said all crimes should be investigated.
Some 660 arrests were made during a recent operation targeting people who had accessed child abuse images online.
However, the BBC understands that as part of that investigation, as many as 20,000-30,000 individuals were identified as potential offenders.
The Child Exploitation and Online Protection Centre (Ceop) - part of the NCA - has estimated that 50,000 people in the UK are involved in downloading and sharing images of child abuse.
"It is uncomfortable because... we want to see these people in the criminal justice system," NCA director general Mr Bristow said.
"But in my judgement, if there are 50,000 people involved, we won't be able to identify all of them and we won't necessarily be able to bring all of them to justice."
He said the agency's priority was to concentrate effort on the "most dangerous people" and those most likely to carry out physical abuse.
But campaigners pointed to a link between accessing abuse images and "contact offending".
A 2012 Ceop report found "compelling evidence" that those who possessed child abuse images should be considered a risk to children.
Tom Symonds, BBC home affairs correspondent
It is an honest admission, which it would have been easier not to have made.
But it is clear that police forces and child abuse experts are dealing with a flood of potential evidence - partly the result of increasingly sophisticated software which can detect the digital fingerprint of abusive images online.
The implication is that police forces and the NCA will have to review their cases to determine those where immediate action is needed to protect children, those where more time can be taken, and those which will simply have to be left on file.
This brings obvious risks. A suspect who has viewed indecent images online but, to date, done nothing abusive in the "real world" may offend at a later date.
Keith Bristow's comments - at a briefing for specialist reporters -  did not include a call for more resources.  There is little doubt others will take up those reins.
The NCA said in July that the 660 arrests made as part of Operation Notarise included teachers, medical staff, former police officers, a social services worker and a scout leader.
Some of the suspected paedophiles had terabytes - equivalent to 1,000GB - worth of data on their hard drives or storage devices.
Mr Bristow said the "most risky" would be targeted first.
He said there would be a "range of interventions" which for some of the offenders could fall short of them "standing in a court".
An NCA spokesman said that included preventative measures and enabling young people to protect themselves online - such as blocking search terms and disrupting anonymous web browsing.
NCA deputy director general Phil Gormley said: "Not every viewer will go on to be a contact abuser," adding that further research was required.
"We need a much more nuanced, much more sustainable approach to this and we need to confront some really unpleasant and horrible truths about human nature."
The NSPCC said the NCA's intervention revealed "an uncomfortable truth about the difficult decisions officers face daily in identifying and pursuing offenders".
Head of strategy Jon Brown said: "The government must make tackling this vile trade a priority in the funding available to the NCA and at a local force level.
"There are clear links between accessing this material and contact offending."
Jim Gamble, who resigned as head of Ceop in 2010, said: "Are we going to say because there's too many we can't do it?"
He added that it was "shameful" Mr Bristow had to "come out and deliver this hard but honest message".
"And the shame belongs with [Home Secretary] Theresa May who has not invested - who has not delivered anything beyond rhetoric to make things better for children where the internet is involved," he said.
Peter Garsden, president of the Association of Child Abuse Lawyers, said a lack of resources was part of the problem.
"The government are now placing blame on the police, whereas the problem actually lies in the Home Office because the police simply don't have enough resources to view and prosecute all the images that are now coming out of the detection system," he said.
Labour accused the government of presiding over a policy which saw "the vast majority" of those downloading child abuse images "not investigated".
"Of course they need to look first for the most dangerous cases, but it seems most cases aren't being investigated at all," shadow home secretary Yvette Cooper said.
"Theresa May created the National Crime Agency... but it's clear now that the NCA is simply not fit for dealing with the scale and seriousness of this problem."
The Home Office said: "We are clear that all crimes should be investigated," adding that the government was "determined to stamp out" what was an "appalling crime".
A spokesman said the NCA had safeguarded or protected more than 1,000 children, making 706 arrests.
Some paedophiles with images of child abuse will escape prosecution, the head of the National Crime Agency has said.