Platini, president of the European governing body, admitted that fans had struggled with the cost and logistical difficulties of travelling to Poland and Ukraine for 2012 and said UEFA wanted to make their lives easier.
"Before, the fans had to go to the Euro, now the Euro is coming towards the fans," Platini said.
UEFA's executive committee voted on Thursday to stage the tournament in an unspecified number of cities around Europe, with bidding from potential hosts due to start in March.
Further details will be decided in the next few months. "There is a blank piece of paper," said the Frenchman, who admitted there was a hint of eccentricity in the decision.
"I love zany ideas... It's an extraordinary challenge," he said.
Any concerns that supporters might have to travel from Lisbon to Astana to follow their team were unfounded, Platini said.
"The fans won't have to travel but we are taking the matches to fans and supporters in quite a number of countries," he said.
"We have met with the Football Supporters Europe recently and we reassured them we will do whatever is possible to make sure that fans get the necessary support when they travel.
"We won't have a team playing in Sweden, Portugal and Kazakhstan with fans chasing all over the continent.
"This is what we explained to the supporters' association, we told them we were going to help them and they had a much more positive attitude."
Fans have had a tough time at major tournaments recently, facing huge costs and travelling difficulties at the 2010 World Cup in South Africa and Euro 2012.
The 2014 World Cup in Brazil is likely to prove even more expensive and challenging for supporters, with most teams playing their group-stage matches in three different venues around the mammoth country.
"It won't be like Poland and Ukraine, with 50 French supporters here and 70 Spanish supporters there," Platini said of the 2020 plans.
"It was difficult to go to Poland and Ukraine and I would like to congratulate the British supporters who went there but perhaps they now have the possibility to go to another country that's closer."
Platini said he would like the final stage of the competition to be held in one city, although the decision would be taken by UEFA's executive committee.
"I'm in favour of the final phase being in one city to give it more importance, that's my idea. The executive committee will decide whether it's a good or bad idea.
"I think this would create a very special atmosphere among the supporters. It will be a week of national teams and it could be a great party."
Platini said that FIFA president Sepp Blatter had told him of a similar plan by late Libyan leader Muammar Gaddafi for the African Nations Cup.
"I got congratulations from the president of FIFA; he said it is a marvellous idea. He said somebody wanted to do it a few years ago with the African Nations Cup and it was Gaddafi," Platini said.