In an interview with the Le Monde newspaper published on Monday, the head of Europe's powerful UEFA football federation said the money was for work he did for FIFA president Sepp Blatter from 1998 to 2002.
Most of the payment, which is being investigated by the Swiss authorities, was only made in 2011. Both Blatter and Platini have denied any wrongdoing over the affair.
Platini provided an extensive account of how that advisory work and related payments were agreed with Blatter, telling the newspaper he has never been good with finances and that he had even short-changed himself in the case in question.
Platini said he had asked for one million francs a year for the work which included reform of the global competitions calendar, work on subsidies for the poorest federations, funding for football projects and a lot of travel with Blatter.
"I've not used lawyers or negotiating agents for ages," the former French soccer star told Le Monde. "It was a man-to-man thing."
Platini said that Blatter had explained that his contract would stipulate an annual sum of 300,000 Swiss francs because that was the top salary rate at FIFA at the time. The rest of the agreed one-million a year would be paid at a later date.
Over four years, such a catch-up payment would have totalled 700,000 francs a year, or 2.8 million Swiss francs.
Platini told Le Monde that when years later he was asked to send a bill for money still due to him, he mistakenly remembered a contract salary sum of 500,000 Swiss francs a year rather than 300,000. He therefore sent a bill for a total of only two million francs for the four years in question.
Blatter and Platini were suspended for 90 days on October 8 after Switzerland's attorney general's office initiated criminal proceedings against Blatter over the 2011 payment to Platini.
Image: Michel Platini