Super sub Olivier Giroud salvaged a point for Arsenal on the south coast – and was then told he is going nowhere in January.
The France striker scored his 17th goal off the bench in the Premier League to cancel out Charlie Austin’s early Saints strike.
He is now level with Manchester United super sub Ole Gunnar Solskjaer as top scorer from the bench for a single club.
The £13million forward, who nearly joined Everton in the summer, has yet to start a Premier League game this season.
When asked if such a big player could be sold in the next window, Arsene Wenger said: “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.”
Giroud has now scored eight Arsenal goals this season – and four in the Premier League.
“He will start games,” Wenger promised.
“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 added: “I always try to bring something for the team when I come on the pitch.
“Today we missed players in the box so I tried to bring it. It was a good cross from Alexis. I tried to be at the right place at the right time.
“We are pleased with this point because it is difficult to play here.”