The North Londoners have taken just four points out of a possible 15 so far in the Premier League and conceded two own goals in a 4-3 defeat at Blackburn Rovers on Saturday.
Wenger, who marks 15 years in charge next month, is enduring one of the worst sequences of his career in England, with Arsenal 17th in the league and just a point above the relegation places.
"Our season depends now on how well we respond to this disappointment and how quickly we can cut out the mistakes we made on Saturday by giving away goals that we should never give away," Wenger told the club website.
"It's very important [to break the cycle]. The Blackburn game is very disappointing and frustrating."
Despite encouraging performances in the Champions League, Arsenal have conceded 14 goals in their five Premier League games, with 12 of them in their last two away matches. They also have the worst goal difference (-8) of the 20 top-flight clubs.
Frenchman Wenger strengthened his squad in the last transfer window, bringing in defenders Andre Santos and Per Mertesacker, who both played on Saturday, but the back four have yet to gel.
Wenger said Santos and Mertesacker "were not especially guilty on the goals. But maybe as a unit we need more time to work.
"A lack of concentration, a lack of communication, a lack of coordination and individual urgency [is behind the goals we have conceded]," he added.
"When you score an own goal, you have to look at yourself. It is never completely out of your reach where you have no chance at all. All the rest, you have to look at yourself."
Alex Song and Laurent Koscielny were responsible for Arsenal's own goals against Blackburn.
Arsenal are expected to field a mixture of first team players and youngsters in their League Cup third round match against fourth division Shrewsbury Town later on Tuesday.
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