The Gunners have failed to score in both their opening games so far this season, which has placed the new signings under considerable pressure.
Last year's Premier League top scorer Robin van Persie left the club two weeks ago to join Manchester United, and Arteta believes that the new boys can't be compared to the Dutchman.
"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. We just need to give them time. It's been two games. Olivier has started one game. It's not fair on him. 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."
Arsenal travel to Anfield to face Liverpool in their next Premier League game on Sunday.