Arsenal have agreed to end the German’s £350,000-a-week contract early so he can join Fenerbahce this month.
The club also came to a similar agreement with defender Sokratis Papastathopoulos, who had six months to run on his deal of around £90,000-a-week.
Arsenal were happy to let the pair go, with neither of them registered for the club’s Europa League or Premier League squads this season.
Arteta, however, hopes the situation does not happen again and the Gunners learn from what has happened.
“You don’t want to get into this position again, that’s for sure,” he said. “Not for the player, not for the club.
“But it’s happening more and more at every club and this situation you can see in other clubs things happening like that.
“I think you have to have that communication open, obviously to prevent it as much as possible and if they happen, just make a decision and don’t try to delay a situation that is not working for much longer.
“Sometimes it’s difficult because the contracts are really close and you have to respect them while you sign them and some days it’s difficult to see how things are going to evolve in six months’ time.
“So sometimes it’s impossible to see what’s going to happen in three years’ time. We tried to resolve those situations early in the summer, to try and avoid what we had but sometimes it’s not possible as well.
“This transfer window and the previous one were really complicated ones and I’d have to assume we have a responsibility with those players and we have to respond to our obligations. That’s what we did until the moment we found a solution for both parties.”
Arsenal will hope their efforts in dealing with contracts will be boosted by the appointment of Richard Garlick, who is currently director of football at the Premier League, as director of football operations.
He will become a member of the Arsenal executive team and will be working closely with technical director Edu, Arteta and academy manager Per Mertesacker.
His responsibilities will include football operations in the first team and academy, all player contract management and relationships with football’s governing bodies.
“Obviously a lot of things happened institutionally at the club and with some of the big decision makers as well,” Arteta said.
“We are trying to create a really strong team with different qualities that hopefully is going to give us more sustainability and success in our decisions.”