A second half Mikel Arteta spot-kick guided the Gunners to a third consecutive league win and lifted them up to third in the Premier League, while the hosts were left stuck in the drop zone.
It has been an impressive turnaround after being dumped out of the League Cup by League Two Bradford two ago with many fans calling for a new manager at the Emirates.
"It was a difficult game but that will give us belief and confidence," Wenger told Sky Sports. "They went for us and it's a good result."
Alex Oxlade-Chamberlain was a bright spark throughout as Santi Cazorla - the hat-trick hero in Monday's 5-2 demolition at Reading - was efficiently marshalled by man-marker James McArthur.
"They stopped us from playing," Wenger added. "We weren't as fluent and sharp as Monday. They had great desire.
"They are in the wrong position in the table. They have a very good midfield and their full-backs did very well."
Theo Walcott continues to be the centre of attention as the England striker stalls over signing a contract extension, wanting assurances over being able to play in his more favoured central striking role.
After producing a couple of dazzling runs, as well as wasting a golden opportunity from six yards from a fine pass from Oxlade-Chamberlain, Walcott did at least create the penalty after being felled by Jean Beausejour in the box.
When asked about his restless striker playing in that role in the long term, Wenger added: "He has potential in that position.
"I'm convinced about his potential to do it there. He didn't get much service against Wigan but his runs were good."