Gyokeres has found the back of the net in just four of his 17 appearances for Arsenal so far, and he was replaced on the hour mark by the returning Gabriel Jesus in the club's 3-0 Champions League win over Club Brugge in midweek.
Arsenal were wooed by Gyökeres scoring 97 times across 102 appearances for Lisbon's Sporting CP.
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But his return of just six goals for Arteta's side -- and his failure to find the back of the net in his past four matches since returning from a hamstring injury -- puts his form in the spotlight ahead of Arsenal's Premier League clash against Wolves at the Emirates on Saturday night.
"There was a lot of excitement because we were bringing a proven scorer that had probably the best stats in Europe," Arteta said of the Sweden international.
"He is a player that comes to a different league, the most demanding league in the world, and what happens if he doesn't score for five or six games?
"That was my only question to him: 'How are you going to react if you don't score in five or six games? Can you cope with that? And then what's going to happen in the next 100 games?'
"And that's what you have to see. The sample is very small. So, leave him alone, let him do what he does best, be behind him and I'm sure things will turn out in the right way."
Gyökeres' last goal for Arsenal came in a 2-0 win at Burnley before he was sidelined for almost a month with a hamstring injury.
But Arteta continued: "We have to put him [Gyökeres] in the best possible condition to explode and fulfil his potential.
"Before the injury, he was in a great place. It took him a while at the beginning because it's a different league with different demands.
"He had no preseason and now he's starting to get some momentum, but the thing that's going to unlock him is goals.
"He needs that for himself, for his confidence, and we're going to judge his performances based on that as well. That's logical, but he wants it so badly as well."
Arsenal host Wolves hoping to extend their lead over Manchester City to five points. City are in action a day later against Crystal Palace.
