The 26-year-old left Madrid for United in a deal worth €75m (£60m) earlier this week after he turned down an offer to extend his contract at the Santiago Bernabeu, which was reportedly worth €6m a year.
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"Madrid never offered him €6m. Their ultimate offer was €5m, which represented a €1.5m payrise. The first problems that arose were the result of financial reasons. He joined Madrid for a certain salary and they left it at that," Miguel Di Maria told El Partido de las 12.
"Angel was never really appreciated at Madrid. It was always as if they didn't want him at the club. They never showed him any affection.
"Angel was tired of always having to prove himself over and over again. He had already proven himself. Madrid have lost a key player, someone who could make the difference at any given moment.
"He is happy at Manchester United now and they treat him well. Their financial offer was also higher than what Madrid had offered."
Di Maria was United's fourth big-money signing of the summer after the previous arrivals of Ander Herrera, Luke Shaw and Marcos Rojo.