The Gunners did complete some business, managing to prize Mohamed Elneny away from Basel, with the Egyptian making his debut in the FA Cup win over Burnley on Saturday.
But Wenger, who predicted the transfer window could be the busiest yet, admitted to a news conference that Arsenal's window had been much quieter than he expected.
"The whole period was much quieter than I anticipated, the fact I'm here now shows we'll still be quiet," Wenger said, ahead of the Premier League match with Southampton on Tuesday.
"If possible, I would have been open to one more but there is a rarity of players."
Arsenal continued their impressive unbeaten record in the FA Cup on Saturday, defeating Burnley in their bid to win the tournament for the third successive time.
And the one player that Wenger did successfully sign for the first-team squad impressed the Gunners boss on his debut, though the Frenchman conceded their would be a bedding in process.
"His first performance was very good," Wenger said of Elneny.
"He made plenty of passes but needs to adapt."