Charlie Austin's early goal had put the Saints in front until the Frenchman's 88th-minute header ensured a share of the spoils at St Mary's Stadium on Sunday.
The goal was Giroud's 17th in the Premier League as a substitute for Arsenal, putting him level with Ole Gunnar Solskjaer as top scorer from the bench for a single club.
Despite not having started a single league game all season, however, Wenger claims that the 31-year-old is too valuable to simply offload midway through the season and is confident that game starts will come the player's way in the coming months.
When asked if such a big player could be sold in the next window, the Arsenal boss replied: "In your question is the answer, because you say he is important, why should we lose an important player? Is it up to him or up to us? It's up to us. It's a remarkable achievement what he has done again today.
"He will start games. I consider Olivier Giroud as a regular player. We have to be grateful that he is part of a great team and one who can come on and make a difference with the right attitude and ability. He is a talent."
Giroud, who is believed to be seeking a departure from the Emirates Stadium in the New Year, has made 13 Premier League appearances for Arsenal this season, all from the bench.