The midfielder's deadline day move to the Emirates Stadium was greeted with dismay by fans of los Blancos, while many of his former team-mates were disappointed to see the German international leave, but Perez insists the player’s departure was his own decision.
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"He could not stand the pressure of Madrid."
The president also responded defiantly to Barcelona defender Gerard Pique's claims that the club’s record-breaking summer spending spree was funded by Spanish bank Bankia.
"What Pique has said is not true," he insisted. "He is a good guy and we should not focus on this point.
"The club paid for the player, with no assistance from Bankia or any other financial institution."
Perez spoke fondly of departed boss Jose Mourinho, who was never far from controversy during his three years in at the Santiago Bernabeu, despite winning both La Liga and the Copa del Rey.
"We had to make a strong point to break the sporting situation with Barca and we got Mourinho," he explained.
"He is a coach who has helped us, we have taken a quantum leap thanks to him, especially in Europe.
"I really like him and he did great things for this club. His opinions and methods of working are correct."