Di Maria was left out of the starting XI for the match against Germany because he was not fit enough to play, but the 26-year-old admits he was unhappy with Real's request.
The Argentine joined United for around £60million last month with the Spanish club's president Florentino Perez saying the winger's demands for a new contract were too high.
And now Di Maria has hit back at the European champions, saying they tried to influence his national coach Alejandro Sabella ahead of the showpiece occasion at the Maracana Stadium in Rio de Janeiro in July.
He said: "There was a letter from Madrid that arrived at 11 in the morning of the match day and we were due to play at four in the afternoon.
"I was putting ice on my leg to be in the final, so I tore up the letter as soon as it was given to me and didn't take any notice of it.
"I didn't care what might happen but it was Alejandro Sabella's decision.
"I didn't want to make any demands of him but I also didn't want to leave the team a man short five minutes from a very important match.
"I suffered a lot that morning, it was the worst thing that's happened to me in my life in football because reaching another final is very difficult, not to say impossible,
"The letter was handed to (late Argentine FA president) Julio Grondona and he said if I wanted to play I should do so anyway. From what I understand it had something to do with insurance."
And Grondona's son agreed that his late father had been handed a letter, saying: "We received the letter signed by Florentino Perez saying he did not allow Di Maria to play.
"We called Di Maria and together agreed to tear it up. We were pressured."
Di Maria, whose goal earned Argentina a 1-0 win over Switzerland in the last 16, suffered a leg muscle injury during their quarter-final match against Belgium and took no further part in the tournament
And Di Maria added that he did not expect to leave the Spanish capital: "I never wanted to leave Madrid. Cristiano (Ronaldo) always supported me to stay.
"Selling me was very good for Madrid to recover all they had spent."