Ivory Coast forward Pepe is facing up to a three-match domestic ban after appearing to headbutt Ezgjan Alioski.
“I will give Nico my full support all the time,” Arteta said. “He knows where he has to improve and we all know his qualities.”
Arsenal travel to Norway to face Molde in the Europa League on Thursday.
Arteta called Pepe’s behaviour “unacceptable” after the incident, but any suggestion the 25-year-old’s career at the Emirates could be over was quickly shot down.
“To say it’s a threat for him to finish his [Arsenal] career, it is not at all like that.” Arteta said of the a £72m signing from Lille.
“I cannot fault his effort at all. You see the way he strives for the team, the way he’s working, it’s been the best since he’s been at the club.
“But there have been some aspects he can do better in because he has the ability. That’s where I’m going to put the pressure on him to deliver what he can do.”
Arteta will be without teenager Bukayo Saka and forward Willian against Molde.
Saka,19, limped off with a dead leg in the game with Leeds, while Willian also picked up a calf injury at Elland Road.
Both players are aiming to return for the Premier League fixture at home to Wolves this weekend.
David Luiz has travelled with the squad after missing out at the weekend following the birth of his daughter.
Arsenal are unbeaten in this year’s Europa League and are three points clear of Molde at the top of Group B.
The Gunners will secure qualification to the knockout stage if they record a fourth successive victory in the competition at the Aker Stadium.
The north London club secured a comfortable 4-1 win over Molde earlier this month.
- Norwegian sides have lost their last four home meetings with English sides in all European competition by an aggregate score of 0-11, with Molde v Arsenal the first such game since Tromso’s 0-2 defeat against Tottenham Hotspur in the Europa League in November 2013.
- Molde had won three Europa League matches in a row before Arsenal beat them 4-1 in the reverse fixture earlier this month – they haven’t lost consecutive matches in the competition since a run of a three games in October/November 2012.
- Arsenal have only been defeated once in their last 14 away games in the group stages of a major European competition (W10 D3), against FC Cologne in November 2017 in the only game they’ve failed to score in during this run.
- Arsenal have scored at least once in each of their last 19 matches in major European competition (43 goals in total); they’ve only had a longer run once – 21 games between October 2003 and November 2005.
- No Arsenal player has scored more goals (2), made more assists (2), taken more shots (11) or created more chances (8) than Nicolas Pépé in the UEFA Europa League this season.