Arsenal broke their club transfer record to recruit Nicolas Pepe as well as completing moves for David Luiz, Gabriel Martinelli, Kieran Tierney and William Saliba at a total cost of around £130 million ($170 million).
"I don't know, I'm not expecting big things," Arteta said when asked on Thursday about potential transfer business.
"I'm expecting big things from the players I have at the moment, the players that are recovering from injuries. That's the biggest expectations from my side.
"If we can find something to help us go through the season in a more balanced way in certain areas, and which is helpful, we'll look at the options."
Arteta, who joined the club last month, has overseen victories in his past two games, a 2-1 Premier League win over Manchester United before a hard-fought FA Cup third-round success against Leeds on Monday.
Arsenal travel to face Crystal Palace on Saturday in 10th place in the Premier League, nine points behind fourth-placed Chelsea.
Ahead of the tie with Leeds, forward Pierre-Emerick Aubameyang used his column in the club's match programme to say speculation he was angling for a move away from the Emirates Stadium was wide of the mark.
"People like making up stories and they should focus on what's happening on the pitch," he wrote. "They talk too much and it does my head in.
"I am the Arsenal captain. I love this club. I am committed to it and desperate to bring it back to the top, where it belongs."
Aubameyang's contract expires at the end of next season and Arteta said any talks over an extension would not take place until the end of the current campaign.
Asked if he was confident the forward would stay, Arteta replied: "I don't know, we haven't discussed that. But I'm confident that he's very happy here because that's what he said in the media.
"I was very pleased to read those comments. He knows exactly what I think about him and obviously he's a massive player for us."