The 27-year-old has scored just six goals in 19 appearances across all competitions and attracted criticism for his peripheral display in Saturday's 2-1 win over Wolves.
Ahead of Saturday's trip to Everton, Arteta was asked to assess Gyökeres' first few months at the club following a €73 million ($85.5m) summer move from Sporting Lisbon.
"The level of attention on him hasn't changed since when he signed to today," Arteta said. "It is normal. Everybody was so excited to bring a nine into the club. We did it. We brought a player with an incredible goalscoring record who had to adapt to the league. He had no preseason.
"The first few weeks were difficult because physically he wasn't in his best state and he is a player who needs that like any other player in this league almost to perform at that level. Then he kicked on, he had a really good period and he got injured.
"Now, I saw a lot of positive things in the last two games that he's done. We need to continue to tweak and understand him a little bit better in certain situations and he needs to do the same. But that's about time and we have full support for him."
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Pushed on whether the best was yet to come for Gyökeres, Arteta replied: "I think so, yes. You can imagine the global impact that you are going to have to deal with when you come to a big club and the expectation is as it is.
"But after you have to live it. Living it is always slightly different to your imagination. He is doing it with a lot of desire. His energy level, his commitment is absolutely top and we are all here to help him because we have all been here, we all need time, there are always moments where the strikers score more goals or less goals. We need to be there for him."
Arteta confirmed Ben White is out for "a few games" with a hamstring injury while Gabriel Magalhães is "pushing hard" for a return to action following a groin problem.
Kai Havertz is also nearing a return from a knee problem but Arteta refused to reveal the target date for his comeback.
"I don't want to say because especially after such a long time after the rehab, I think we need to be cautious and we need to go really firmly with every step that we take along the way to make sure that when he's back, he's back and he's back for the long term," Arteta said.
"He's progressing really well and quite fast in the last few weeks. We are really positive that if everything continues like that in the next training sessions, he's going to be with us."
