Giroud set his side on course for a 2-0 victory that moved them four points clear at the head of the Premier League table when he dispossessed Saints goalkeeper Artur Boruc and scored mid-way through the first half of Saturday's game. The forward then stepped up to convert a late penalty, taking his tally of goals for the season to seven in the league and ten in all competitions.
"Other strikers will tell you, 'I am not obsessed by scoring goals,' but if they don't, they are sick! It is a relief on their shoulders," said Wenger. "I believe as well that Olivier didn't expect himself to score so many from the start of the season, but it can only boost his confidence."
Wenger added: "Olivier is a positive character who is always ready for a battle. He is maybe completely different to the rest of the team in that he gives us so much with his physical presence, with his link play, which he has improved tremendously. He has the mental qualities and a positive attitude."
The win ensured Arsenal bounced back after suffering the disappointment of defeat by Manchester United immediately before the international break.
"I am convinced that after a break like that, the character is tested," Wenger added. "Can you win when you have to in a season like that, straight away again after a big defeat to Manchester United? That was really at stake for us.
"We have improved our defensive stability. After an international break, you have always two challenges: one is to get the team to focus again as a team, because we have been spread all over the world and you have very little time to get the focus point right.
"The second is physical, because they all come back in different levels of fatigue; some have not trained a lot. The first point we got right; the team were highly focused. We suffered a bit physically, but overall the concentration was there."
No Boruc blame
Southampton manager Mauricio Pochettino offered Boruc his full backing following the Poland goalkeeper's embarrassing mistake. Boruc was caught in possession after rejecting the chance to clear first time when he received Nathaniel Clyne's back-pass and Pochettino said: "It's true that we were unlucky when we conceded that goal.
"There is nothing more to analyse. We all saw what happened and we can draw our own conclusions and we have to just move on. It happened. I fully support all of my players. These things can happen in football. We have to keep on looking forward and keep on working the way we have been working."
Pochettino refused to attach any blame to the former Celtic man and said that Boruc's mistake would make him a better player. "It's the way that we play," said the Argentine. "That's what I demand of him and what I demand of all my players. There is nothing more I can say. It's just a bad day.
"I think footballers need to be able to learn from these mistakes. They need to be able to live with these mistakes and know these things can happen, accept them and move on. And from our point of view, we just offer our complete and 100 percent support for him. And keep talking to him, working with the entire team and moving on."