The Colombia international was strongly linked with a move to the Bernabeu stadium this summer but the deal did not materialise.
Falcao instead joined Manchester United on a season-long loan from Monaco on the final day of the transfer window.
"The deal with Real Madrid did not happen because if you have money and you go to the market to buy a shirt or a pair of trousers, you have to decide whether to buy it or not," Falcao's father Radamel Garcia is quoted as saying to Colombian radio station LA FM.
"Real Madrid chose not to.
"I don't know, I have the feeling they wanted the player for free with a number of conditions.
"In any case, they bought the trousers and shirt they wanted and they considered that to be better.
"We have to accept it."
Despite apparently being turned down by Real, the 28-year-old forward had plenty of offers on the table, according to his father.
"The clubs that showed an interest in him were Juventus, Manchester City, Liverpool and Arsenal at the last minute," Garcia said. "Fortunately, he has arrived to Manchester United, a great club.
"Thank God everything came through with United.
"Radamel is a person who has given a lot in Europe and has always deserved the best for all the effort, all the sacrifices he has made during his football career.
"United is the most important team in England and one of the most powerful from an economic standpoint.
"Now it's his (Falcao's) turn to give his best, to be ready and continue to win titles."
Garcia is confident his son will adapt quickly to the Premier League just as he did at Monaco, whom he joined in June 2013 from Atletico Madrid..
"Fortunately, he has adapted to European football," he said. "In the teams he has been since he left (River Plate) Argentina (in 2009), his integration has been very easy.
"He was very happy at Monaco but unfortunately, they changed the original plan and decided to sell the players they had bought."
Falcao scored 11 goals in 20 appearances for the Ligue 1 side last season before sustaining a knee injury in January that kept him out of the World Cup.
The South American will wear the number nine jersey at United and is expected to make his debut at Old Trafford against Queens Park Rangers on September 14.