The France international came off the bench at the Liberty Stadium this week but was unable to help the Gunners avoid a shock 3-1 loss to the Premier League strugglers.
Giroud has been tipped with a January move away from the Emirates Stadium, with Chelsea said to be interested in his services, and Wenger admits the striker could leave before tonight's transfer deadline.
Asked whether Giroud could have played his last game for Arsenal, Wenger said: "It's a possibility but all that will be decided tomorrow morning. We will inform you once that is more definite.
"It's a tribute to Olivier (that he played) because he is a guy who gave great service to the club, he never let us down on the commitment front and saved us many times.
"I have absolutely no doubt, when I ask him if he is ready to commit and he says yes. I have no problem with that and put him on because it was needed. Unfortunately he couldn't help us.
"I took him from Montpellier and made him a strong international player for France. We have come together through good and bad but always his behaviour was top, top class."