The Gunners were frustrated in their attempts to land Vinicius Junior, who chose to sign a new contract at Real Madrid, and also missed out on the signing of another top target Morgan Rogers, who joined Chelsea from Aston Villa earlier this summer.
Arsenal completed the £75m signing of Bruno Guimaraes on Saturday, with the Brazil international making his first appearance for the club in Wednesday's friendly against Como at the Emirates Stadium, but their efforts to add firepower are ongoing.
"There is more that we want to do because every time we have an opportunity to improve the squad and bring more quality and depth to the squad, we need to do that," said Arteta.
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"We are actively trying to do so. The thing in the market is that it doesn't just depend on you. We are very clear on that.
"But the approach, the will and the desire of the club, that's unquestionable. We want to try to do that. But we cannot promise that we're going to do it because it doesn't only depend on us."
The Premier League champions are interested in Atletico Madrid's Julian Alvarez and Paris Saint-Germain's Bradley Barcola but their search for a marquee attacking signing appears set to continue deep into the transfer window.
"I think for the margins to improve, there are very few players in the market that are available to do that and bring that to the club," added Arteta.
"But again, we are actively looking to improve that and we're going to try."
Asked if Arsenal's wage structure could be affected by signings of that stature, Arteta added: "I'll leave that question to [sporting director] Andrea [Berta] and the board.
"My job is more to focus on getting the best out of the players that we have, to create that connection between them and to make every player feel important, regardless of the wages."
'Bruno was pushing to play'
Arteta was pleased to hand a debut to Guimaraes against Como, as he impressed as a half-time substitute only four days after his arrival from Newcastle and could now be in contention to start in Sunday's Community Shield against Manchester City.
"Let's see," said Arteta. "He only had three training sessions, but he looked good. He was really pushing to play some minutes.
"I think he wanted to get his debut and the feeling of playing in front of our fans immediately.
"And you sense immediately, I believe, a strong connection at play that is going to make us better."
Arteta coy on Lewis-Skelly future
Myles Lewis-Skelly has been linked with a departure from Arsenal following the arrival of Guimaraes. He was the subject of an enquiry from Chelsea and is also a long-term target for Manchester United.
But the 19-year-old scored Arsenal's goal against Como, after which he made a heart gesture before holding his hands together towards the home fans.
"It's good to score a goal, you should be emotional when you score a goal," said Arteta of his celebration. "He's a very emotional player. I remember when he did all the gestures on the pitch [last season]. I'm not going to talk about any speculation.
"If there is a speculation about our player, it's a good sign. That means that we attract attention and they're doing a good job.
"I think he had a really good pre-season. I think we asked him to play in a different position, because he played more as a six, because we lacked central midfielders, obviously with international duties, and I think he had a really consistent pre-season."
