''You will have to ask the club for reasons why they sold them, but at the same time he didn't think he was getting the opportunities he deserved and luckily he has come to us.
''He is an important player and he is going to be very good for the team and the way we play. I hope he can help us fight against the big teams in the Premier League.''
Creative talent Cazorla has impressed since his move from Malaga in the summer of 2011, and was reported to have attracted interest from Atletico Madrid.
However, the 28-year-old maintains it was never something on his mind. He added in the Spanish newspaper: ''The Atletico president said there was nothing in this, and I always very relaxed about it.''
Arsenal have responded well since their opening-day 3-1 home defeat by Aston Villa, where defender Laurent Koscielny was sent off, to qualify for the group stages of the Champions League and then beat Spurs before the international break.
France defender Koscielny has become an integral part of the Arsenal's rearguard and developed a good understanding with Germany international Per Mertesacker, as captain Thomas Vermaelen continues to recover from a back injury.
The 28-year-old, signed from Lorient in July 2010, believes he has now fully adjusted his game to match the demands of the hustle-and-bustle of the English top flight, learning how to best respond to any untimely errors.
''I feel that I'm better, better in quite a lot of areas. I have more confidence in challenges, I feel that I hurt opponents more,'' Koscielny said in an interview with French newspaper L'Equipe.
''I need to be more aggressive, though, but in all areas I have gained in physical presence. However, you will never hear me say I am an undisputed first-choice for club or country.
''Repeatedly playing in big games allows you to acquire experience. I still make mistakes, a bad clearance, bad positioning, but rarely do I play badly for the full 90 minutes. It is just that after a mistake, you have to be able to start again with the simple things.''
While Özil was Arsenal's marquee signing of the summer, free transfer Yaya Sanogo hopes to soon make an impact on the first team.
The France under-21 forward, brought from Auxerre in July, has made a couple of substitute appearances so far, and admits he will have to ''toughen up'' for the challenges ahead.
Sanogo said on Arsenal Player: ''I will need time, it's a new way of life, a new league and it will take time to adapt. It's something I will manage.
''I will have to toughen up and improve my strength, that's part and parcel of such an intense league as the Premier League.
''My main aims are to come here and learn, progress in the game and learn my trade with such great players. Now I'm training with them, I'll gradually make progress.''