The decision came as business analysts warned that tourists would steer clear of the city, costing the economy some £4bn.
Inter Milan were due to play Leicester City, Portsmouth, Norwich City and Crystal Palace later this month. Leicester City is now threatening to take legal action against the Italian club for the lost revenue, which could be as much as £250,000.
A statement on Inter Milan's website said the decision to cancel the tour had been taken because they did not want to "add to the activities of the emergency forces there, who are already very busy at this time".
It added: "Football has taken a step back because of increasing serious events which touch the sensitivity of everyone."
Mr Livingstone said: "It is a very silly thing to do because it is playing the terrorists' game. They want to change the way we live."
He added: "The idea that there might not be an attack back home [in Milan], that they are more safe there than here, is a complete illusion. As we have seen from the horrifying news from Egypt, nowhere in the world is safe."
Crystal Palace, due to play Inter on Wednesday, said they are "saddened and angered".
One undeterred football team is the Iranian national squad, in Britain playing against Millwall, Queens Park Rangers and Portsmouth.Reuse content