The Argentina midfielder sealed a £59.7 mllion move to Old Trafford on Tuesday and signed a five-year deal with the Premier League club.
Di Maria has long since been linked with a move away from Santiago Bernabeu, but the 26-year-old claims he was forced out of the club and would have preferred to have stayed with the European champions.
In an open letter to Real fans published by Marca, he said: "My time at Real Madrid has come to an end. It's impossible, in just a few lines, to put all I have gained here, but this letter is my way of explaining how I'm feeling now that I'm bidding the club farewell.
"Over the four years I have had the honour of wearing this shirt, I have felt nothing but pride about everything that has happened and all I have achieved together with my team-mates.
"Sadly, now I have to go, but I want to make it clear that this was never my wish. I've always wanted to progress, as anyone else does in their job.
"I went to the World Cup after winning the 'Decima' with the hope of getting some signal from the Club Management, but it never came.
"Many things were said and many lies circulated. They always wanted to pin the idea of leaving the club on me, but that's not how it was.
"Unfortunately, my football isn't to someone's taste. The only thing I asked for was a fair deal. There are many things that I value and a lot of them have nothing to do with my salary.
"I hope to find them at Manchester United, one of the biggest clubs in the world, with which I'm hoping to make history."
