There are fears that it could be a precursor to a campaign of cyber attacks by the Kremlin, and the Foreign Secretary said Britain must take "every possible precaution" to guard against it.
"I'm afraid the Syrian war will go on in its terrible, miserable way".
British warplanes took part in the strikes, which destroyed sites suspected of hosting chemical weapons development and storage facilities.
But Johnson stressed the "overwhelming purpose" of the mission was a response to a series of chemical attacks in recent years.
His comments come ahead of a what is expected to be a heated Parliamentary debate on the Government's decision to launch strikes with France and the United States without first seeking the approval of MPs.
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He said the investigations had been completed by the state Crime Branch and a charge sheet had been presented in the court. The girl was kidnapped on January 10 and her body was found on January 17.
"There is no proposal on the table for further attacks because so far, thank heavens, the Assad regime has not been so foolish to launch another chemical weapons attack", Johnson said.
"Finally the world has said "Enough is enough", and I think it's important that we understand the limits of what we are trying to do..."
He also did not rule out further attacks against Syria if the Assad regime continued the alleged use of chemical weapons.
Last night the UN Security Council has rejected a resolution tabled by Russian Federation calling for condemnation of the "aggression" by the United States and its allies against Syria.
On the same show, Jeremy Corbyn expressed his unease over the strikes and criticised the prime minister for not recalling Parliament to vote on the issue.