Pepe was reportedly on a number of European clubs’ radars over the summer, but in the end he chose to complete a £72m switch to the Gunners.
The winger’s return of 37 goals in 79 appearances for Lille, and 23 in 41 last term, meant high expectations followed him to the Emirates.
Yet so far it has been difficult for him in north London, with his only goal in eight appearances coming from the penalty spot in a home win over Aston Villa.
Arsenal fans were most concerned by their club-record signing’s performance in Monday’s 1-1 draw away at Manchester United, nevertheless, which saw him give the ball away 17 times before being replaced in the final 15 minutes.
Pepe has drawn plenty of criticism after that showing, but Emery has told Gunners fans to be patient with the French-Ivorian as he adjusts to the Premier League.
“I am sure Pepe is an amazing player, I am sure he is going to have a big career here,” he said.
“He needs time. A lot of players when they came here, the first month, the first year is not easy for them.
“He still needs to play, get confidence, know progressively better the other players, our work.
“With adaptation, some need less time and some need more. But every player needs time when they arrive here – young players or players as important as Pepe.
“He needs to play, he needs to train, he needs to be with us, he needs to also understand better English and French with us, with the players.
“I am speaking with him and he is telling me he understands me when I am showing him some moves individually and also speaking about how we want him to play with us.
“But really it is one process and I am sure he is going to be, step by step by playing matches, getting better with his performance.”
Arsenal are gearing up for their second group-stage outing in the Europa League tonight.
Standard Liege are due to visit the Emirates in Group F, with kick-off scheduled for 8pm.
Emery’s men are looking to record their second straight victory after winning 3-0 away at Eintracht Frankfurt last time out.