A decade later British Prime Minister Margaret Thatcher gave a speech in which she made a similar point, declaring that terrorists depend on "the oxygen of publicity."
Nothing had underlined this better than the Munich Olympics in 1972 during which 11 Israeli athletes were taken hostage by Palestinian terrorists. All the Israelis were killed either by the hostage takers or during the course of a botched rescue operation.
The hostage-taking was covered by TV networks from around the world who came to cover the games but ended up providing coverage of a terrorist event that unfolded before the first truly global audience for such an attack. More than any other single event, it brought the Palestinian cause to the world's attention.
On 9/11 untold hundreds of millions around the world watched the attacks as they happened in New York and near Washington on live television. Osama bin Laden himself listened to live coverage of the attacks on BBC Arabic radio in his hideout in Afghanistan.
The 9/11 attacks, which took place in the city that is many ways the capital of global media, thrust bin Laden and his terrorist group al Qaeda onto the world stage in a spectacular manner.
But in neither the Munich Olympics hostage-taking nor on 9/11 did the terrorists have actual control over the content of the coverage, which was instead determined by those media networks covering the event.
So what we saw unfold in the attack on the mall in Kenya is something quite new: a terrorist group shaping the media coverage of the event in real time through the medium of Twitter.
The next logical step will be for terrorists to cover their deadly operations using their own real-time live video feeds linked to sites such as Twitter, Facebook or YouTube.
If that happens, terrorist attacks will become a form of theater in which terrorists not only get to write the play but also act as the primary producers of the coverage of the event.
A dark glimpse of this brave new world could already be seen in Al-Shabaab's assault on the Nairobi mall.
Unfortunately, that may not be the end of Shabaab's terror attacks outside Somalia. On Thursday Shabaab posted the following chilling tweet: "The mesmeric performance by the #Westgate Warriors was undoubtedly gripping, but despair not folks, that was just the première of Act 1."