The Gunners have so far recruited England defender Ben White from Brighton as well as midfielder Albert Lokonga from Anderlecht and Benfica full-back Nuno Tavares.
They have also been linked with a host of other names as Arteta looks to build a squad capable of improving on back-to-back eighth-place Premier League finishes.
The likes of James Maddison, Aaron Ramsdale, Martin Odegaard and Houssem Aouar have all been listed as reported targets.
But Arsenal open the Premier League season away at newly-promoted Brentford on Friday night with just the trio of signings landed earlier in the window.
“In this first period of the transfer window I think we’ve done a few things we wanted to do and it’s going to help us to get the squad in a much better place,” Arteta said when asked how he judged Arsenal’s transfer window to date.
“There is still a bit of the window to go, so I’m sure things will happen either way. We identified what we wanted to do and how we can strengthen our team short, medium and long term, and what we needed to achieve that.
Fans need to be excited and they need to see a team that is capable of competing with those teams because our history is related to that.
“We defined the profile of player that suits the model that we have at the moment at the club that can sustain our financial position, and we made three movements in relation to that.”
Despite being sure of further action, Arteta did say he was “willing to work” with the players currently at his disposal.
He also conceded Arsenal need to excite their fans by proving they can compete with their traditional rivals, suggesting any transfer business could happen all the way to the close of the window.
“Fans need to be excited and they need to see a team that is capable of competing with those teams because our history is related to that,” he said.
“Nobody can deny that. That’s the aim and that should be the objective.
“It is something at this time that is not possible to do on August 12 but is possible to do on the last day.
“Whether you are happy bringing the player in or not is more important. I think everything is related to who we bring in, who is out, our capacity to hold foreign players in the squad. There are a lot of question marks still to be resolved. It’s still pretty open.”
In terms of outgoings, Arteta said Joe Willock is in a position to determine his own future as a potential transfer to Newcastle rumbles on.
“The situation is that he’s our player and we’ve held some conversations because it’s not only about what we want to do,” he added.
“It’s the player’s interest and the role that a player can field in a squad and in a club.
“What he’s done is put himself in a really strong position where he can choose a little bit with more options of what his future could look like, and this is what we’re trying to define right now.”