For some the natural response was to ask "How could this happen in our society, what have we done wrong, how can we put it right?"
For others the automatic reaction was to find people to blame, to look at others rather than themselves, to seek vengeance rather than enlightenment.
Half of today's newspapers splash on the Intelligence and Security Committee's report on the murder. Its key conclusion was that while there were signs of the killers' intent and mistakes by the security services - who were on their case - little, if anything, could have been done to prevent the eventual atrocity.
That is not the stuff of splash headings. Far better fodder can be found in the section of the report relating to "graphic" Facebook messages between Michael Adebowale and an extremist in Yemen.
Ah yes, Facebook has blood on its hands. Facebook kept quiet about the plotting. It "never flagged up one of the killers crowing of a lust to murder a soldier" and is "still failing to co-operate with the probe" reports the Sun.
"Incredibly, Facebook had already disabled seven of Adebowale's accounts - five of which were flagged over links to extremism - without informing security services," writes the Mail. Facebook is a "safe haven for terrorists," highlights the Telegraph.
As several papers say, Facebook has 31 million users. That's quite a lot of accounts to keep tabs on. That FB had acted against several of Adebowale's profiles suggests that it is aware of the uses to which the site can be put and accepts a level of responsiblity for people's security.
That's not quite the same as being an ad-hoc arm of any particular country's security services, spying on its customers and snitching on them to the authorities. Is that really what our national newspapers want it to become? Papers that have been outraged by invasions of journalists' privacy by the police? Papers that have made much of how all-pervasive social media businesses have become, how they intrude into our lives and share our personal details?
Let's hope not. But the opportunity to have a go at those wicked "tax-avoiding internet giants" is not to be missed. The Mail asks why Cameron "cosies up" to them, saying that concerns about their links with Downing Street "reached fever pitch" in the summer with the appointment of Joanna Shields to the Lords. It must have been the fine weather that caused SubScribe to overlook this scandal.
Lady Shields had been a big cheese not only with Facebook but also with Google and Bebo. What is more Cameron is a close friend of Rachel Whetstone, Google's head of communications, who is married to a man who used to be a policy chief at No 10.
What has this got to do with Fusilier Rigby? Heaven knows.
The Mail also reports suggestions that publication of the ISC's findings had been manipulated to push through draconian anti-terror powers, but it gives greater prominence to demands that the Communications Data Bill, which would have required internet companies to keep records of every site their customers visited. That seems more relevant to the Rigby report - but instead of presenting those calls straight, the Mail puts them under the heading "Snowden leaks cost lives, say terror experts".
And so instead of addressing a legitimate story in detail, the paper has used a great chunk of the space allotted for its coverage to beat its own ideological drum.
Thank heavens for the more rational coverage of the Guardian, Independent and Times. And thank heavens, in particular, for the commonsense of Alan Travis who writes in the Guardian:
It is not the job of the internet companies to intercept the content of their customers’ emails or other exchanges any more than it was the job of the Post Office to read everyone’s letters. Postal workers did not steam open suspicious letters – that was the job of the police special branch, and the distinction is important.
Only the state can have that power and up to now most internet companies have shown themselves willing to respond to specific requests to monitor targeted individuals as long as it is backed by a legally enforceable warrant issued...
No such request was made in the Woolwich case because the security services regarded Michael Adebowale...as a low-level threat and so “intrusive action would not have been justified”. It is hard to see how, if it was not justified for MI5 to take intrusive action to monitor his online activity in order to pick up the threat to kill a British soldier, it could be justified for a US internet company to do so.