Pepe left Arsenal last week to join Turkish side Trabzonspor after having his contract terminated by the Gunners.
The winger became the ninth Arsenal player to suffer that fate in recent seasons, just four years after he moved to the Emirates Stadium for a then club-record fee of £72million.
Arteta has defended the decision to terminate Pepe’s contract, while adding that it was not the Ivorian’s fault that he had to cope with the pressure of a huge price tag.
“I wasn’t involved in the process of that deal,” said Arteta. “But what I can say is that he was a phenomenal boy who tried really hard and tried his best so it’s not his fault the amount of money we paid at the time.
“When things aren’t working you have to move on. There is no point trying something when it’s not working for either so I think it’s best for both parties.”
Pepe was not the only player to leave Arsenal late in the summer transfer window, with centre-back Rob Holding completing a move to London rivals Crystal Palace.
Asked if he was sad that Pepe’s time at Arsenal never worked out, Arteta said: “Yes, but obviously there are moments for players.
“Not only for him but for Rob leaving and the others who have left on loan.
“You have an emotional attachment with them and you have tried to get the best out of them, but there are periods and sometimes you can love the player but there is a player who plays in this position as well who does so well.
“There are many factors but we certainly wish them the very best and hopefully they can fulfill their dreams somewhere else.”
Arsenal have made an unbeaten start to the season and they are next in action on Sunday when they travel to face Everton.
The Gunners have a poor record at Goodison Park and they have not won there since 2017, when Arsene Wenger was still in charge.
“Sometimes we cannot avoid a battle,” said Arteta. “There are certain balls that you have to prove and they have a certain style of play that they are extremely good at.
“We have a very different one and when you are trying to impose your way of playing it is about trying to make sure your opponents’ strengths are completely hiding and yours are coming out every time.”