The Argentina international was already heavily linked with a move away from Madrid in the summer of 2013, but he eventually stayed at the Santiago Bernabeu side because of the Portugal international's presence.
Di Maria did leave Madrid this transfer window, however, as he joined Manchester United in a deal worth €75 million after losing his starting berth to James Rodriguez.
"The truth is that I have a great relationship with Cristiano Ronaldo and I stayed at Madrid last season thanks to him," the Argentine told ESPN Radio.
"I left Madrid in the best possible way, by winning La Decima. In my farewell letter, I said exactly how I felt from the first day at the Bernabeu.
"I am grateful to Manchester United for meeting Madrid's demands. But I don't feel any extra pressure because I'm the most expensive player in the Premier League.
"The Premier League is more physical and about strength, whereas Spain was more about football. It's a very strong league, though. Van Gaal has told me to try to adapt as quickly as possible."
Di Maria made his official United debut in the scoreless draw with Burnley at the weekend.