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The Gunners are without a win in four league games and have failed to score in the past three.
They are fourth in table, five points behind leaders Leicester.
"We have to catch that back and we have a difficult programme, especially away from home," Wenger told the club's official website.
"We need to respond quickly away from home now."
Arsenal have only won once in the league this year, drawing 3-3 at Liverpool and 0-0 at Stoke, and losing 1-0 at home to Chelsea prior to Tuesday's match.
Asked if he was worried his team's season would tail off, Wenger said: "It's too early to say that. It's true that we've had a stuttering start in 2016.
"Our January was bad, starting from the last minute at Liverpool, and then at Stoke.
"Where we especially have a big deficit is in our two home games. We played with 10 men for the whole game against Chelsea and today we created 10 chances and didn't score."
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Leicester's 2-0 win over Liverpool means they retain top spot, while Arsenal have dropped below Manchester City and Tottenham, who won at Sunderland and Norwich respectively on Tuesday.
"Leicester won again and now I am sure that everybody will take them very seriously, especially in the media, so they will be under pressure as well," said Wenger.
"But we have not to look too much at Leicester or Man City. We have to win football games. We have to focus on how to respond quickly and win our next game, that's all we can do."
The Gunners created a number of good chances against Southampton but were unable to convert them, with Saints goalkeeper Fraser Forster excelling.
"The quality of the chances we created today, considering it's a Premier League game, was high," added Wenger. "The quality of the finishing was poor.
"Our finishing is very bad at the moment - we have played three league games now without scoring a goal. In all those three games we had chances that we didn't take. At that level it's important."
Arsenal boss Arsene Wenger acknowledged his side are playing catch-up in the Premier League title race after their goalless home draw with Southampton.