Having gone nine years without a trophy, Arsene Wenger's men have now landed two in the space of three months.
An FA Cup triumph at the end of last season got the ball rolling again, and Manchester City were swept aside 3-0 at Wembley on Sunday to open the new campaign in style.
Arteta admits confidence is flowing again around Emirates Stadium, with summer strengthening suggesting that Arsenal will be contending for major honours this term.
Those inside the camp insist they will accept nothing less, with there a determination on their part to keep the winning feeling flowing.
Arteta told Sky Sports: "We want to progress from what we did last season. It was a long spell without trophies, we put it right last season but it's not enough for this club.
"I think we have to aim for bigger things and hopefully starting the season like this will help to boost the confidence, the belief, and I think we are heading in the right direction."
Arsenal put in a commanding performance against City, with Santi Cazorla, Aaron Ramsey and Olivier Giroud getting the goals on a productive afternoon.
Arteta believes an impressive showing bodes well for the season ahead, with one result showing that Wenger's men are capable of competing with, and overcoming, the best in the business.
The Spanish midfielder added: "Facing one of the top teams, the champions of the Premier League last season, and with some of the games we had against the top teams when we didn't perform that well, today was a good opportunity to put it right.
"We showed that we can compete again."