Mr Gormley said he was "profoundly disappointed" that so many suspects had been arrested over this type of crime and said a harder look needs to be taken at the high numbers of people accessing child abuse images.
The "dark web" is internet content that is not listed by normal search engines. Users will often use payment methods such as virtual currencies to help avoid detection.
The NCA deputy boss said: "As our understanding increases of the scale and the nature of this type of offending enabled by the internet, there is a challenge. There is a challenge for law enforcement, there is a challenge for policy makers.
In previous cases, officers have used undercover tactics, including posing as potential victims to lull sex offenders into showing their true colours.
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Claire Lilley head of online safety at the NSPCC said: "This is an important two pronged operation which has rescued children from abuse and also identified many previously unknown sex offenders. Direct action like this sends a strong message to those who subject children to harrowing sexual assaults that they can and will be traced and prosecuted.
be able to arrest our way out of this problem? I doubt it. We are going to need to think about all sorts of measures around prevention, disruption, protection and pursuit.
"There are very significant volumes of people viewing this material in this country and abroad.
NCA deputy director general Phil Gormley said the crackdown, the biggest ever operation of its kind, involved alleged paedophiles who used the so called "dark web" as well as traditional internet access.
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Mr Gormley said sex offenders should realise that they cannot avoid detection while using the internet, even the dark web.
to abuse children."
"This operation has been about protecting children who are victims of, or might become victims of, sexual exploitation. Children are victimised not only when they are abused and the images first taken, but at every subsequent time that image is viewed by further offenders or distributed," he said.
The NCA said suspects include doctors, teachers, scout leaders, care workers and former police officers. In total 39 of those arrested are registered sex offenders.
Suspected Merseyside paedophiles arrested in police crackdown From St Helens Star
He said: "The alternative is not to look under the stone, and we cannot afford not to look under this stone."
Officers have searched 833 properties and examined 9,172 computers, phones and hard drives.
"So while this operation must be rightly applauded we should view it Reebok Kamikaze as yet another warning sign that far more needs to be done if we are to stem the sordid trade in these images, which are often used by those who go on Saucony New Balance
who were safeguarded were in the "care, custody or control" of the suspects, and included 127 who were deemed to be at immediate risk of harm.
"We are going to need to understand as a society how we are going to confront this issue. We are not going to be able to arrest our way out of it. The numbers are significant, the volumes are huge."
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