The Netherlands striker scored his first goal for Manchester United in a 3-2 victory over Fulham on Saturday after completing a £24m move from Arsenal to Old Trafford earlier this month.
Van Persie scored 30 goals in 38 Premier League games for the Gunners last season, and Arteta conceded that no striker will be able to match the Dutchman’s feats at The Emirates over the last 12 months.
“You can’t replace Robin. To do so is impossible because he’s such a special player,” Arteta said.
“Manchester United went for him at the age of 29 – what does that say? It says there aren’t many bigger talents in the world.
“It doesn’t matter who is brought in for Robin. You can’t ask anyone to be as good as him.”
Wenger bought Giroud and Podolski earlier this summer ahead of Van Persie’s departure, but the duo are yet to net for Arsenal.
The 30-year-old midfielder urged Gunners supporters to be patient with the pair, with Arteta confident the goals will soon arrive.
“We just need to give them time. It’s been two games. Olivier has started one game. It’s not fair on him,” added Arteta.
“It could all change for him, just like that. Last week, Olivier had a massive chance to win the game and he would have been the hero.
“Against Stoke, Lukas had a chance. He looked good on the left on Sunday, cutting in and causing problems. He had a couple of chances.”
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