The Gunners have made an inconsistent start to the Premier League season after winning four and losing four of their first eight matches and the Spanish manager believes his team should be doing better after beating Manchester United away from home before being bought back down to earth by Aston Villa.
Arteta told Arsenal's website: "We're a long way, I'm afraid.
"It's part of a process. The results have to be immediate, and the challenge we have with the club we are representing is that we have to win as quickly as possible every game in every competition.
"So far we have played 14 games in all competitions this season, we won 10 and lost four and the four of them have been in the Premier League, so it is a little bit imbalanced."
Arteta added that he is firmly focused on the "bright future" for the north London club.
He explained: "There are a lot of things to do, short term and medium term, we have seen a lot of changes not only on the pitch but structurally as a club as well.
"It has been difficult, it has been a challenging time in the last three or four months, a lot of things have happened.
"We have to settle and everyone has to realise where we are now, but I see the future as really bright. I am a really positive person and I tend to learn much more when things don't go well and we have a defeat like we had the other day that really hurt after the performance we had at Old Trafford.
"We have to understand why it happened, be really critical first of all with myself and try to understand the players better and give them more solutions to win more football matches."