Pepe, who became Arsenal's record signing when he was signed for a reported fee of £72 million in 2019, joined French side Nice for the rest of the season on Thursday.
"He's tried to deal with (the price tag) in the best possible way. Obviously, he's not responsible for the price a club pays for him," Arteta told reporters ahead of his side's game against Fulham.
"He needs minutes, he's been talking to me about it. I can't guarantee that now. We decided for every party it was the best decision to allow him to go."
Arteta said the London club had been planning for the possibility of Pepe leaving and how to replace him.
"If we can implement the plan that we have, we will try to do it," Arteta said. "We've been preparing for the last two months and now we will see."
According to a report in The Times on Monday, European football's governing body UEFA have put Arsenal on a watchlist of teams in danger of breaching Financial Fair Play rules, but Arteta said the club were operating within their means.
"We are compliant, and I don't know where that is coming from...we are very clear with the limitations we have, and how we have to deal with things," Arteta said.
The Spaniard will take charge of his 100th Premier League match as Arsenal manager when the league leaders host seventh-placed Fulham on Saturday.
"Time flies. Such a privilege to be at this club and reach this number. Hopefully, we can extend that for a long period and bring joy and a lot of wins," Arteta said.
