Arsenal have been linked with a number of players during the transfer window, and it was initially expected that they would bring in an experienced striker to replace the injured Robin van Persie.
However, Wenger focused his efforts on defence, first bringing veteran Sol Campbell back on a free transfer and then looking to tie up a deal for Fulham defender Smalling. After Manchester United ended up clinching Smalling's signature, though, it appears there will be no further arrivals at Emirates Stadium.
"Manchester United got Smalling in the end," he said. "I am sorry because we were very close to getting him and we were on the case very early.
"I wish the player well. At the end of the day, it is important he has a good career. In both clubs, he has a good chance to make a great career. The most important thing is he does that."
He added: "It is not impossible (to sign a player before window shuts), but at the moment it is unlikely."
Meanwhile, Wenger has backed Campbell to rise to the challenge of facing Manchester United on Sunday if Thomas Vermaelen does not recover from his injury in time.
"Sol is ready, if he has recovered well. I have to assess him today, but normally he will play if Vermaelen doesn't play,'' he said.
"The good news we have on Vermaelen is that there is no fracture. We have to assess his knee today - there is still a small chance that he plays on Sunday.
"We will do the maximum to get him fit, but at the moment it looks unlikely. It should be a very short-term injury, and at the latest he should be ready for the Chelsea game."
He added: "Sol has experience and he likes the big games. He can turn up if needed and experience helps in these kind of games. Sol can cope with Rooney.
"I believe Sol has worked very hard and credit to him, every day he was motivated to push himself and he is quite fit. He looks fit."