Pepe has struggled at times since joining Arsenal in the summer of 2019 from Lille for a club record fee of £72million.
More recently, however, the Ivorian has begun to show his potential and his goal on Thursday night against Slavia Prague was his second in his last three games.
Pepe also claimed an assist in the win over Sheffield United on Sunday and Arteta believes the winger has come through his period of adaption at Arsenal.
The Spaniard is now backing the 25-year-old to be a hit in north London and said there are no excuses for him not to be.
“I think he needed to do that, yes,” said Arteta when asked about Pepe changing his mindset.
“He needed a period of adaptation and that is gone now. So we cannot rely on adaptation again, now it is about performance and he can do it.
“He has got the players to support him, a manager that trusts him, he has got all the staff that are willing to help him and all the team mates who really like him because he is a really likeable character, so there are no excuses.”
Arteta has revealed he had private conversations and individual sessions with Pepe to help develop him.
But he added too: “Probably the biggest thing is when you see that you don’t play and what you have to do to play and then when you do it, you play.
“Nico has this ability – it depends on him, we can help him as much as we want but he needs to have the right mindset and consistency to do what he can do.
“Because that is the level that we are going to ask of him, the level I am asking of him – if it is something below that he is not going to play.
“But if he does what he can do he will have a big chance to play because he has got incredible ability.”