The Gunners chalked up their 1,000th Premier League goal under Wenger during Saturday's 4-1 win over Bolton, who had defender Gary Cahill sent off just after the hour at the Emirates Stadium.
Defender Laurent Koscielny opened the scoring - and his Arsenal account - with a bundled close-range effort, before a tame back-header led to Bolton's equaliser just before the break.
That, though, was just about the only notable mistake from the French centre-back pairing, with fellow new arrival Sebastien Squillaci making his debut following a £6million switch from Sevilla because of a minor Achilles injury to Thomas Vermaelen.
It was inconsistencies in defence which proved Arsenal's undoing last season, when they shipped 41 goals - some nine more than champions Chelsea, while Manchester United only let in 28.
However, Wenger believes signs are positive that unwanted trait is set to be reversed.
"We know we can score goals and as a team we improve from season to season. We are more mature, and of course our challenge will be to be sound at the back," Wenger told BBC Sport.
"We have now played two difficult teams, at Blackburn and against Bolton, when defensively we were quite strong.
"Everybody can score goals in our team, but I feel we are more stable defensively and are slowly getting there."
Wenger believes his young side passed another character test, having been good value for their lead after creating a string of chances - and on another day Andrey Arshavin could have had a hat-trick before the break.
Marouane Chamakh headed the hosts back in front following Johan Elmander's 44th-minute equaliser, before Cahill was shown a straight red card for going through the back of the Moroccan striker right in front of the dugouts.
Alex Song brought up Arsenal's milestone with a well-taken goal after 78 minutes, his first at Emirates Stadium, before substitute Carlos Vela stroked in number four.
On a sour note, it remains to be seen just how much damage was suffered by midfielder Abou Diaby, who went off less than 15 minutes after coming on, following what looked a poor challenge from Paul Robinson.
Bolton boss Owen Coyle, though, took exception to what he felt was a key decision by referee Stuart Attwell - who famously allowed a "ghost goal" during a match between Watford and Reading two years ago - just before Cahill's sending off, and remonstrated with the 27-year-old official after the final whistle.
"It is there for everyone to see," Coyle declared.
"The pictures will clearly show Lee Chung-young is fouled right on the edge of the box. I don't think it is a penalty, but it is certainly a free-kick.
"Then within a few seconds they have played the ball on the counter-attack and we are down to 10 men when Cahill gets sent off.
"I am not going to get myself into trouble by saying too much, but I am sure anyone who knows anything about football will know that was clearly a free-kick.
"Ultimately we have paid a heavy price for that big decision."
The match highlights will also show, however, Bolton goalkeeper Adam Bogdan making sure the score was not more harsh on the visitors with a string of impressive saves.
The Hungarian was making his first Premier League start in place of the suspended Jussi Jaaskelainen, and left an impression on his manager.
"When he was called on, he made some big saves," said Coyle.
"We have got high hopes for Adam and I felt for him because he certainly did not deserve to concede four goals."