Blatter also told British Prime Minister David Cameron he was "impressed" by the country's bid for the 2018 World Cup finals.
The FIFA president, on a one-day visit to London to meet Cameron, told a select audience in Downing Street afterwards that England had shown the world the way by driving hooligans out of the game and he wished other countries had the safe modern, stadiums England had built in the last 20 years.
"If this had been the case in Genoa yesterday we would not have had the problems we had at the (Italy v Serbia) match. This is a big legacy, an important legacy you have given to the world."
The Euro 2012 qualifying match in Genoa was called off after only six minutes due to crowd trouble, an echo of England's bleak times of 20 years ago.
Blatter told Cameron: "Your predecessors were in a very difficult situation during the years from 1985 to 1989.
"I don't want to speak about what happened then, but instead the reaction you have made.
"You have given to the world security in the stadiums. You have built all your stadia, there are no fences and everyone is sitting.
"You did it here - and now we say where are the hooligans? They are not in the stadiums and this is a compliment to your government and your predecessors."
He praised England's World Cup bid, emphasising that although he knew England could "organise the World Cup tomorrow," their legacy message that it was a "World Cup for the world" had impressed him.
"The situation is such that your bid has impressed me personally and I will report this to the Executive Committee when we meet during in October."
DIVERSE NATION
Cameron told Blatter that one of the first things he did when he became Prime Minister in May was to re-confirm the new government's full support for the bid.
"I hope you see that England has got what it takes to host the greatest tournament on earth. I hope you can see how much our country wants this. We are passionate about it. We want it really badly."
"We are the most diverse football nation in the world and we have travelled so far in kicking racism right out of football and that is one of the reasons why I believe we can make 2018 such a success."
England are one of five nations bidding for the 2018 finals which are expected to be awarded to Europe. Russia, Spain/Portugal, Netherlands/Belgium and the United States are the other bidding nations.
Those countries are also, technically at least in the hunt for the 2022 World Cup finals which are likely to be awarded to an Asian country from either Qatar, Japan, South Korea or Australia.
FIFA's executive committee will announce the winners of both bids in Zurich on December 2.
