The centre-back had to pull out of the squad due to his 'detailed pre-planned training and medical programme', which has managed his back injury problems in recent years.
Oxlade-Chamberlain told Sky Sports News: "It is really disappointing for us. Obviously, Rio is an amazing footballer.
"He plays for a club like Manchester United so the experience that he can bring to us from his club team and the level he plays at - Champions League football - would be brilliant.
"But the players that will come in and the players in the squad are more than capable to do the role and fill in with good quality and good experience."
"I do not think there is any reason why he should not," added the Gunners player. "He is an amazing player and has been for so many years.
"But, obviously, it is not for me to say. I am not the manager. But, for me, Rio is an amazing player and would be a great asset to the squad."