The Frenchman came on as a 76th minute substitute despite talks of an £18m deal for his services being agreed with Chelsea before kick off.
However, service is what Giroud did not get against Swansea and he was unable to turn the tie as a brace from Sam Clucas and a goal following a Petr Cech howler canceled out Nacho Monreal's opener.
When asked by Sky Sports 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."
Wenger refused to comment on the imminent arrival of Pierre Emerick Aubameyang as his replacement, adding: "We will know more about that tomorrow morning."
The Arsenal manager lamented that at times his side showed comical defending at the Liberty Stadium and maybe the £60m would be better invested in shoring up that area of the squad rather than more luxury attackers.