Giroud's 88th-minute header cancelled out Charlie Austin's early goal to earn the Gunners a share of the spoils at St Mary's.
The goal was Giroud's 17th as a substitute for Arsenal, with the striker yet to start a Premier League game so far this season.
Reports on Sunday had claimed that the experienced striker had made the decision to leave the Emirates in January as he looks for more regular football, but Wenger scoffed at those claims, saying that it is the club's decision whether they sell or not.
"He is important - why should we lose an important player? It is up to us [and not Giroud]," Wenger said following the draw.
"He will start more games. I believe as well it's always the same when you have many good players, some of them cannot play.
"The question you get is always why does the guy who is good not play? Because if you take him on you have another guy who is good who will not play, it is as simple as that."