The Gunners have spent the international break licking their wounds after defeat at Manchester United.
Olivier Giroud struck twice for the Gunners in the 2-0 win and Wenger said: "We have a long way to go, but we have the ambition, the focus, the concentration and the desire are there.
"We played against a good Southampton side today who tried to stop us from playing. They did it well and in the end we couldn't take our chances, but we took advantage of their two mistakes.
"They are a team who is very well organised and our technical quality helped us to get away with a win today."
Wenger added: "I am convinced that after a break like that, the character is tested. 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."
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