Florentino Perez says the Argentine winger had 'financial requests' the European champions couldn't satisfy.
The 26-year-old completed a £59.7 million move from the Bernabeu to Old Trafford this summer, though Perez insists the La Liga giants did their utmost to keep the winger in Spain.
Indeed, the Madrid president says they made Di Maria the 'best offer' they could, only for his 'financial requests' to prove too high.
According to Perez, Real Madrid would have been left 'unbalanced' had they accepted all of Di Maria's demands.
"We made the best offer that we could to Di Maria and he didn't accept it," he told reporters.
"Hence, we brought in James [Rodriguez], one of the best players at the World Cup and the Golden Boot award winner.
"Di Maria and all of those that have left have our gratitude and respect. A player that is under contract and leaves is because he wants to. Real has always respected contracts.
"Di Maria had financial requests that I considered legitimate but we couldn't satisfy them. I reiterate that we made him the best possible offer.
"With the exception of Cristiano (Ronaldo), Di Maria would have been the highest paid at Real Madrid.
"Had we accepted his financial demands it would have created an unbalanced treatment that would have put the club's stability in danger.
"Di Maria left to Manchester for a fee that we considered fair and that is why the transfer was completed. We wish Di Maria the best professionally and personally."
The winger has since gone on to make his debut for Manchester United in a 0-0 draw with Burnley but, more impressively, scored once and registered three assists for Argentina against Germany on Wednesday night.