Following the Carabao Cup final defeat by Manchester City earlier this month, defender William Saliba confirmed he would not be joining up with France because of an ankle injury.
His centre-back partner Gabriel then withdrew from the Brazil squad with a knee problem.
They were later joined by England forward Eberechi Eze (calf), Norway midfielder Martin Odegaard (knee) and Netherlands defender Jurrien Timber (groin) - who all missed the cup final defeat at Wembley through injury - as well as Belgium forward Leandro Trossard (hip).
After players joined up with their respective countries, five more from Arsenal withdrew - England trio Declan Rice (knock), Bukayo Saka (knock) and Noni Madueke (injured his knee against Uruguay) as well as Spain's Martin Zubimendi (knee) and Ecuador's Piero Hincapie (undisclosed).
Arteta said his players were "desperate" to play for their countries.
"When you are fit and available to play for the national team, you have to play," he added.
"It makes us so proud that we had that many players in the national team.
"Players are desperate to play for their nation. I know how important it is to them. We are fully supportive of that and when we can do it, we do it."
Premier League leaders Arsenal are in FA Cup quarter-final action on Saturday as they visit in-form Championship side Southampton (20:00 BST).
Arteta confirmed Eze will miss the game through injury, but Odegaard and Timber are in contention to return, while Madueke's injury is not as bad as first feared and is a doubt.
Asked how many of those 11 players who withdrew from international duty will be available for selection against the Saints, Arteta added: "You will see. I will let you do the speculation. You can judge afterwards.
"We are in a position right now where we need to make the strongest line-up we possibly can to win every competition.
"We are two or three games away from the FA Cup and we know how important that competition is for us."
