Pepe was sent off during the goalless draw at Elland Road on Sunday for butting heads with Leeds’ Ezgjan Alioski and Arteta said his action was “unacceptable”.
The winger is now due to be banned for the Gunners’ next three Premier League games, but he is able to play in Europe and could get a chance to make amends on Thursday.
Pepe travelled with the Arsenal squad to Norway on Tuesday and Arteta is ready to play him after he apologised both publicly and privately.
And asked if Thursday was the perfect time for Pepe to show he has learned his lesson, Arteta said: “Yes, absolutely.
“We have all had disappointments in our playing careers and obviously now we are frustrated because when you play against a team like Leeds for a long time with 10 men it makes a huge difference.
“He had a really good reaction. The way he apologised, the way he understood his responsibility and hopefully tomorrow we can see the player we want to see have a good reaction and help his team.
“I will give Nico my full support all the time. He knows the things he has to improve, but as well we all know his qualities.
“He has some responsibility, I have some responsibility, which is to get the best out of him and get the best position for him, the best areas for him to do what he can do with the ball.
“I can’t fault at all his effort and if you see any of his stats the way he is trying for the team, the way he is working, it’s the best since he’s been at the club.
“But there are certain aspects he can do better, because he has the ability and that’s where I’m going to put the pressure on for him to deliver what he can do.
“But to say it’s a threat for him to finish his career [at Arsenal], it’s not at all like that.”
Arsenal head to Molde looking for their fourth win in a row in the Europa League, which would see them confirmed as Group B winners.
They have struggled for goals in the Premier League, but they have scored nine in three matches in the Europa League.
Former Tottenham midfielder Christian Eriksen has been suggested a solution as he is reportedly keen to leave Inter Milan.
But asked about that, Arteta said: “There are a lot of players out there that can improve any team, but obviously we are not going to discuss individuals.”
Free agent Jack Wilshere has also been linked with a return after he said it would be a “dream” to come back to Emirates Stadium.
The midfielder left West Ham in the summer after mutually terminating his contract and is currently in Dubai keeping fit.
“We haven’t analysed that situation,” said Arteta, when asked about Wilshere coming back to Arsenal.
“What I can say about Jack is as a player, as a team-mate and as a person, that I rate him really highly. But unfortunately at the moment we haven’t looked at that, we are focused on the players we have and trying to do the best we can with them.”