The Gunners, who face Turkish club Besiktas in the first leg of their playoff round tie next Tuesday, have been busy, signing striker Alexis Sanchez, defender Mathieu Debuchy and keeper David Ospina, as well as recalling Costa Rica striker Joel Campbell after a loan spell.
Wenger said the mood in the camp has been "serene" but could still try and add to his resources before the end of August.
"Will I still do something? I don't rule it out. Our finances are still healthy, but we want to go through in the Champions League group stages to do that," Wenger told a news conference on the eve of Saturday's Premier League opener against Crystal Palace.
"Number-wise we are maybe a little short in some areas of the game but the depth of the squad is very good."
"I'm happy with the players I signed, with their quality and their attitude," added the Frenchman.
"There hasn't been a massive change, but we signed Debuchy, Sanchez, Ospina and (Calum) Chambers, all of them have integrated well mentally into the team.
"We are not destabilised and I feel it's a strong reinforcement of our squad."
Arsenal are tipped to challenge title favourites Manchester City and Chelsea this season, but Wenger said it was difficult to gauge the relative strength of their rivals until the transfer window is closed.
"A lot can happen until August 31," Wenger said. "That's why I always said that it will be better that the transfer window closes before you play the first game, it would be much easier for everybody.
"You have six or seven teams. You have the top four and then you have Man United and Everton; how well will Tottenham respond? I don't know. But Everton was very dangerous last year as well and they could be candidates.
"We are in a stronger situation, but we are still facing clubs who have unlimited resources and who are in the same situation of strength."
Wenger, whose side beat champions Man City 3-0 in the Community Shield last Sunday, looked relaxed as he contemplated the season ahead without the weight of a long silverware drought on his shoulders following last season's FA Cup triumph.
"It has been the calmest environment certainly," he said of the build-up to the season.
"I am long enough in the job to know that the reality is (Saturday), the toughness of the Premier League, how much can you turn up there and produce a performance.
"All the rest is good to have, it is a good basis, a good spirit, a good quality in our sessions. But the reality is when we start the game at 5.30pm, to show that we are up for it and ready for a battle."
(Reporting by Martyn Herman, editing by Tim Collings)
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