Pepe has played the last five games in all competitions as the Gunners boss looks to get the best out of him.
He said: "There is a click for him in his mentality, how he is approaching every training session, importance of every action in the game.
"I really like his attitude. What he's done in recent weeks has been much better.
"He still has a lot of room to improve and he's willing to do that so I'm expecting him to go to the next level very soon."
He said: "Well, I think Mat played a really good game. For the first game he played with us after little training I think he was really good.
"I really like the way he reacted because to concede a goal on your debut so early and still react the way he did it shows a lot of character from him.
"So that's why we brought him here because he has to be an option, and he has to keep pushing Bernd."