Real president Perez faced criticism in some quarters for allowing the Argentina international to join Premier League side Manchester United for a British-record fee of £59.7 million last month.
Perez responded by claiming he took the decision because an agreement could not be reached with Di Maria, who he said wanted to be paid a similar salary to that of Real superstar, and Ballon d'Or holder, Cristiano Ronaldo.
However, Di Maria insists that is not the case, adding that his move to Old Trafford came about because he believed Real were keen to sell.
"I heard what he [Perez] said. To earn what Cristiano does I'd have to win the Ballon d'Or," he told Radio America.
"I never said I wanted to leave Madrid. I never wanted to. During the World Cup I thought only of the World Cup and I don't know where things said in the Spanish papers [about wanting to leave] came from.
"Whatever they say, they got €75m for me which is very good for the economy of Real Madrid. They got back what they spent.
"Nobody said anything to me or my representative about staying so we thought Madrid wanted to sell. Before the World Cup there was no offer from Madrid."
Di Maria also claims he ignored a request from Real to miss the World Cup final, although injury prevented the 26-year-old from featuring in his country's 1-0 defeat to Germany anyway.
"There was a letter that arrived," he continued. "I was getting treatment to try to play in the final and I knew if I played I had a 90 per cent chance of getting hurt.
"When I got the letter I ripped it up. I didn't speak to anyone from the club. I didn't care. Eventually [then Argentina coach Alejandro] Sabella made the decision and it was for the best."
