The government will examine what powers it requires following the brutal Woolwich killing, the Communities Secretary said on Friday.
But Pickles said he did not believe any measures in a mooted communications data bill, dubbed the "snooper's charter", would have prevented the death of the soldier in Woolwich.
The plan was dropped by the government under pressure from the Liberal Democrats because of concerns about personal privacy.
Pickles told BBC Radio 4's Today programme: "What I am certain about is a free society is vulnerable to an unexplained, heavy violent attack, whether it was as our dear friends in Norway faced a couple of years ago a white supremacist or whether what we faced on the streets of Woolwich, a blasphemy and distortion of Islam."
Several politicians, including former Defence and Home Secretary John Reid who is now a consultant for G4S, and anti-terror expert Lord Carlisle, have called for the government to revive the charter.
Senior Tory points out 'Snoopers Charter' was never off the table, just parked 'cos of Lib Dem opposition. May could use #woolwich to revive— Beth Rigby (@BethRigby) May 23, 2013
Former Home Secretary Jack Straw told The Huffington Post UK: "This raises the issue about increased communication data. We do not know at this stage that the absence of these powers was a factor in their being at large.
"I hope the Intelligence and Security Committee will look at it."
He added: "No doubt the same people describing it as a snooper's charter will be saying 'why didn't the security services pick them up'?"
The fact that the men were known to the security services did not mean they should have been picked up, he added.
Lord West, the former First Sea Lord and security minister, told Sky News that having a database of people's internet and phone usage would have helped security services monitor the men.
“That information is extremely important for our security services to be able to pin down people, find out who they were linked with, find out who radicalised them.
“We need to know this information, and I do think that the Communications Data Bill that was due to come through but has been put on pause by the Deputy Prime Minister, I think that’s a terrible mistake.”
"I know of nothing that would suggest that provisions that were in that bill would have made any difference in this case or would have saved the life of the young member of the armed forces.
"I think it's probably too soon to assess the powers we need but, once the investigation is through, both aspects of the security services and aspects of the policing of these two individuals will be thoroughly investigated and no doubt recommendations will come out of that."
Pickles was asked earlier if Prime Minister David Cameron's response would have been the same if the attack had been a random killing rather than linked to extremist elements of Islam.
Pickles said: "I think the Prime Minister would have been very heavily criticised if a British soldier had been murdered on the streets by two people with clearly, from their own mouths, a political message, and it's important we understood what was happening and try to make an assessment of whether this was just the beginning of a series of events that would escalate the violence and, pleasingly, that appears not to be the case.
"I think the Prime Minister acted wisely in coming back and I think he would have been very heavily criticised had he not done so."