The German ace joined the Gunners on a £42.5million deal on deadline day but admits that he felt on the weekend he would remain at the Santiago Bernabeu.
"At the weekend, I was certain that I would stay at Real Madrid," he told German Football Association's official website.
"But afterwards I realised that I did not have the faith from the coach (Carlo Ancelotti) or the bosses. I am a player who needs this faith and that is what I have felt from Arsenal, which is why I have joined.
"I am a player who needs this faith and that is what I have felt from Arsenal, which is why I have joined.
"I am really looking forward to it because I have the faith of the coach. I had spoken to him at length on the telephone, he explained his plans and that he has faith in me - that is what I need as a player."