Moyes lasted less than a season in the United before being sacked.
"It certainly had to be difficult to replace a figure like Sir Alex Ferguson, the most successful manager in football's history. It was impossible, in fact," Mata wrote in his new book, Suddenly A Footabller: My Story.
"The first time I met David was seconds after coming out of a helicopter, as this is how I arrived at Manchester United 's AON Training Complex. Pretty cool, I know. Bond-style.
"He was waiting for us to land and welcomed me and my family with a big smile and these words: 'Welcome to a fantastic club, a massive club. The biggest club there is."
"Then he took us to his office and we talked. 'Juan, I know what type of player you are, I know what you can bring to the team. I need a player like you who can link the play.'
"When I arrived, late January, the campaign was already halfway gone and things were not going too well. We were seventh in the league.
"Results were not materialising and the atmosphere was not ideal.
A few months later, after some more disappointing games, the club decided to part with Moyes and chose Ryan Giggs to look after the first team until the end of the season.
"The Moyes era had been much, much shorter than expected.
"Just like André Villas-Boas at Chelsea, he tried his best, as he is a committed and dedicated manager, but we were just not performing well and results were not good enough."